Everyone you talk to in the UK is going to tell you the schools in America are a disaster and nowhere near to the level of their UK counterparts. Americans are fat and stupid and cannot possible compete intellectually with the rest of the world, blah blah blah. Of course, their knowledge of the American education system is based on biased media reporting in Europe and Hollywood movies, so please take their words with more than a grain of salt.
Many expats have come with fears about education, only to be shocked and surprised by the quality they have received in the US. Active and engaged teachers, enthusiastic students, and extra curricular events that will make your head spin. Some even dread returning to the UK and have literally said "what the hell were they doing in school back home". However, others have landed in areas where the schooling is faltering and rushed to find private schools, regardless of the high tuition expenses. Schools often mirror the communities, so in many impoverished areas you can expect the schools to also be struggling.
It's often said but worth repeating here: as with everything about the United States, you need to remember that this is a HUGE country. What applies to one town in one small state in one tiny corner of the country cannot, even remotely, be extrapolated as a 'perfect example' for the rest of the country. In addition, education is handled by state and local governments, not the federal government in Washington. There is no national curriculum and every state can teach different things. As such you are going to see incredible, nearly 180 degree differences between schools in some parts of the US vs others. This is really one of those things that depends in large part on where you live--what state, what city, what school district, even what STREET (as students are assigned to schools geographically).
A few terms
Public school means a government funded state school. Please note the difference in usage to the UK.
Charter school is a government funded school, but managed by a private entity.
Magnet schools are schools that focus on a particular field, such as arts and music, or math and science, drawing students from across different school boundaries.
Private school is an independently funded school.
Parochial school is a private school funded and maintained by a religious organization (most are affiliated with the Catholic Church).
School district is a regional government entity that is in charge of schools in a neighborhood, city, multi-cities, or county level.
Immersion School is a school in which class are taught in two languages, one day English and the other day Spanish, French, Mandarin Chinese, etc. Predominantly in major cities.
Elementary school is generally grades K-4 or K-8 (think "primary school" from a UK perspective)
Middle school, where it exists, is generally grades 5-6 or grades 5-8.
Junior High School, where it exists, is generally grades 7-8 or 7-9.
High school is generally grades 9-12. Also called "secondary school" in some areas.
Before you Leave
A lot depends on your state that you will be living in, but things that should be brought would be:
a) your school transcripts, describing the course content and grade. Class syllabus and other descriptions of the curriculum will be helpful as the schools attempt to place your child in the right year (more on this in a minute).
b) vaccination records, as all states require certain jabs before allowing you to enroll your children.
In many states you will not be allowed to send your child to school until you prove that they are uptodate on their vaccinations. Just to repeat: Vaccinations are taken very seriously in the US. Kids will not be allowed into school without them, and in some states parents have been hauled before a magistrate and given the choice of vaccination or fines. As it can take awhile to get those records together, one of the first things you should do in preparing for your move is get a list of your child's vaccination history. You should google 'school vaccination requirements <name of your state>' to see what is required. The list is extensive and includes a few not part of the standard procedures with the NHS (such as Hepatitis vaccination). There are exemptions for religious reasons, but it is worth noting that should you intend to immigrate full-time the USICS will NOT recognize these exemptions from the necessary vaccinations, so if that is in your long term plans you might want to plan ahead.
The two main ones that people encounter are varicella (Chicken Pox) and Hepatitis B. Chicken pox can often be excused if your kid has had them, but Hep is something you are probably going to need to get started before you leave as it is a 3 shot procedure. Shot one, Shot two 30 days later and shot three six months later. Most schools will let you in if you have started the process for Hep. Some schools may also require HPV vaccinations.
US School Structure
Schools in the US are generally broken down as:
Kindergarden (4 and 5 year olds)
Elementary School (Grades 1-2-3-4)
Middle School (Grades 5-6)* these sometimes merge *
Junior High School (Grades 7-8)* these sometimes merge *
High School (Grades 9-10-11-12) generally ages 14-18
University (Freshman, Sophmore, Junior, Senior)
A School District is the governing authority for multiple schools in an area. It could be a city, multi-city, or even county school district depending on where you reside. Most of the policies on attendance (cachements), admission, graduation, etc are set by the school district, but these must comply with state education laws (curriculum requirements, school choice laws [allowing cross district transfers]) and federal education laws on testing and civil rights (special needs requirements). When searching for information on your school, your first stop will likely be the school district website for your town or area.
My Kids are Ahead of their US counterparts
A common question that comes up is 'my child is a 'year ahead' because of the difference in starting times in the UK vs. the US'. The UK starts their kids at 4 where as generally the US is at 5. However, it is worth noting that in many US school districts kids do start at 4 as well, in what is known as "pre-K" or "K-4". It is usually a half day session and followed by full kindergarden when they turn 5. But most US parents do not start their children in school until they turn 5.
While your kid may be "ahead" in terms of number of years in school, generally you'll find educators will place children, especially at the younger ages, in classes with other students their age rather than other students who have been in school as long as your child has been in school. Emotional and physical development is often as important as academic development. At higher years, there may be an opportunity to be placed in a higher grade than the student's age, but it can be a double-edge sword. While you may be keeping up with your 'year' back in the UK, many members on this site have reported it is not advised as their children have had difficulty keeping up with their peers here in the US. There are considerable differences in the methods of teaching in the US vs. the UK such that eventhough a student might be a 'year ahead' when they arrive in the US they often report 'feeling left behind' by the pace and manner of instruction.
There really isn't a right / wrong, one size fits all answer to this question. It's going to depend a lot on your child--how mature are they, what sort of academic environment they prosper in, and how are they developing physically. Being the smallest and youngest child in a class can have an impact. The issue of when to start school, and whether to hold back a student (sometimes called 'red shirting' based on the American sports practice of holding back a developing player a year before they start playing, kind of like sending a footballer out 'on loan' to another team) is a hotly debated one not only in the US but in the UK as well. This recent article summarizes some of the studies on the matter, and it might be worth reading if you are considering a higher grade for your child:
When to Start School -- NY Times.
Even back in the UK the discussion about a later start age is being debated. Many researchers prefer the European model of age six, and schools in Finland, which consistently score amongst the best in the world, start at age 7.
 "Delay school entry until six, researchers urge"
 "Is five too soon to start school".
This is also an interesting discussion on the subject (despite a bit of ranting in the middle of the thread): http://britishexpats.com/forum/lounge-7/getting-put-down-grade-school-643985/ Strongly recommend reading through the comments of others who have gone through the experience, some pushing their kids up a year and some keeping them at their US year, and the various successes (and a few failures) that have come with that. Some have reported their child fit right in, sometimes even becoming the honor student despite being a year younger. Others have come in and discovered in just a few weeks that it was a terrible decision and moved the kid back to their age appropriate year.
In short, you really need to look into this issue specifically related to your child, the school you are coming from (and may return to) and the school you will be attending in the USA.
Useful link to school year comparisons between UK and US. This gives the ages and years of both US and UK systems for comparison.
School start dates and "cut off" dates.
Generally schools start between mid-week in August to the first week in September (after the Labor Day holiday). School will continue to late-May / early June, depending in part on when the school started and in many parts of the country on how many "snow days" they had during the winter (for every day missed due to snow, the children's school year can be extended by a day in May/June). This can be very important if you are planning a Summer holiday the day after school is out, only to discover that the school year has been extended by a week due to a blizzard a few months prior.
Here is a state by state breakdown of when to start school. Generally the cutoff date is September 1, be XX years old by September 1. However some states have a December or January cutoff date.
While your kids may be able to name a dozens Kings and Queens of Europe, they probably can't name more than a few Presidents of the United States. American history will be required, as well as 'civics' (American government) and whatever courses they may have had in these subjects in the UK are more than likely not on par with the ones their American classmates are having. Reading, math and science is taught somewhat differently in the US than the UK, and some parents have reported their 'top students' in the UK have needed a year or two to catch up to the way they do things over here before they return to the top of their class. There are also 'little differences' that will add up, such as different spellings and different usage of common words (sidewalk vs. pavement, 'the hospital' vs. hospital), etc. along with things like currency calculations of "nickels, dimes and quarters" instead of "pence and pounds".
One area of concern is at the high school level in that mathematics is taught somewhat differently in the USA than the UK. In the US, you study a math subject each year of high school from introduction to near-university levels. For example, Grade 9 will teach everything about geometry, Grade 10 everything about Trig, Grade 11 everything about statistics, etc. In the UK system you get a more spread out approach, with one year covering multiple subjects. This can make transitions at the high school level somewhat more complicated.
There are several online websites that you can use to "track" your child's US education against their UK peers. The Hamilton Trust runs a resource for teachers and for parents, which includes class plans and worksheets that are based on the UK national curriculum. You can print out some of these from time to time to make sure you are uptodate against the kids in the UK.
Schools are primarily controlled by local government. A 'school district' will cover an assigned area, such as a town or even a county, and then a 'school board' of elected or appointed officials will govern the operations. A 'superintendent' is generally the presiding officer for the district. Each school has a 'principal' in charge of the school, and then one or many 'vice principals' in charge of different functions such as staff, student affairs, etc. 'Guidance counselors' are available to help with college preparation, academic selection, and more often than not, personal issues affecting students.
There is no set national curriculum for students. Each state sets a basic requirement that students get so much math, so much science, so much physical education, etc, and then the local school boards design their classes to meet those requirements (Algebra in grade 7, geometry in grade 9, etc). When moving from the UK, it is usually advisable to meet with the school officials and go over your child's coursework so they can be fitted into the right classes upon arrival.
It is *very* important to note that schools in the US are generally funded by property tax revenues from the surrounding areas. In areas with high property values, there are higher taxes (and sometimes) more revenue available for the local schools. In areas of low property values, there is less funding available for the school district. Each school has an assigned 'region' that it covers and unless you live in area of 'school choice' you'll probably end up sending your kids to the nearest geographical school (**pay attention to this when buying/renting a home**). Living on one side of a street instead of the other can often make the difference between school A and school B.
In many urban areas, the public schools subject from many of the same social ills of the surrounding area, and many of the more well-off parents opt to send their children to privately run schools (for a considerable fee).
Due to standardized testing, there exists a number of website that will allow you to "compare stats" between schools (for better or worse if you like such testing). One such site is http://www.greatschools.net/ where you can get specifics on each school in your area and for specific info about NY city schools can be found at inside schools site.
It's been mentioned before but which school you go to is entirely dependent on where you live. The exact address, down to which side of the street. Your school district will publish maps (often somewhat confusing) that says 'if you live here, you go to this school, if you live there, you go to that school'. There are no wait lists, shortlists, 'spots' or things like that--if you live in the school's boundaries, you are going to school there. If you move in the middle of the school year into the school boundaries, you are going to school there (with very few exceptions). Rather than move kids from one school to another school districts generally try to maintain the 'neighborhood school' idea, often times building additional classrooms or using temporary structures to handle any overload.
In some areas and states, there exists what is known as "school choice". This allows parents to choose schools that are not in their geographical cachement. However, the rules for this vary from state to state, and in some places the 'local' kids close to the school get first choice and then if there are any slots open it is made available to other children from surrounding areas. You'll need to check your school district's website to see if school choice is an option.
When you arrive and get settled, find out what school you will be attending from the school district and contact their front office. Explain to the receptionist that you just moved to the area and you would like to get the kids enrolled. They'll probably have some forms you can fill out and if you want, you can try to make an appointment with the principal or vice principal to go over your children's previous coursework and what classes they will be taking in the next year (probably necessary if you want to 'up' your kids to a higher grade level based on the fact they started earlier in the UK, etc).
NOTE: Immigration status has nothing to do with your eligibility for school. By law, schools have to take everyone, even those without legal visa status. What can be a 'problem' is when you start throwing around US Immigration words like 'I am not a permanent resident (i.e. I do not have a green card) and the receptionist at the front desk hears 'I'm not a resident in this school district' (and thus not eligible to enroll). Please note that the use of 'resident' and 'status' and all the other terms from your immigration efforts are not the same usage that the school district will use, and that it can cause confusion if you use those terms.
Private and International Schools
Private schools exist across the country, though they are far more common in the Northeast and in urban areas where public schools have faltered. In some larger areas you will find international schools that draw students from other countries who are working toward an IB degree rather than a US high school diploma. In places such as Washington, DC, which is filled with many diplomats from around the world, you will find the whole gamut of British International, French International, German International, Saudi International, etc. Schools for students from around the world.
Cost is a major issue at many private schools, and some schools are considered academic all star camps and others are places where "rich folks dump their troubled children". Doing some research is definitely advised before pursing the private school route.
There are a few private British schools in the Eastern part of the USA, but that's about it for those wanting a UK-based education system (GCSE and all that). Some schools in the US do follow the IB diploma standard though.
Long Term, US or UK?
Something to consider is what is the long term goal for the education of your child. Will they return to the UK for University, or are they going to go into a trade, or do you think they'll state in the State and finish education and find a job. Keeping up with the peers back in the UK isn't really that important if your child has expressed a desire to study at an American university. Of course a great deal depends on your own visa and financial situation (and eventually, they will be required to have a visa or right to live in the US when they become 'of age') but it is something to consider when planning your move.
If you are only coming for a year or two, you may want to get a copy of the curriculum and lessons for the 'year' your child would have been attending and supplement their education in the US with whatever it is they may be missing back home.
Sports and Extracurricular
Sports, at the high school level, is a very important part of the school life, and in many places, the general community. In some areas of the country, "Friday Night Lights" (i.e. American football games played on Friday nights) is the social to do of the Fall. Crowds of 10,000 come out to watch some football games (yes, that is not a typo--10,000+ people!).
But it's not just Football, Basketball and Baseball. Most schools have a full offering of sports, from golf to tennis to track and field. In addition, each year there is a 'physical education' requirement that means students will have to switch into running clothes and play some physical activity for at least an hour a day (this is a throwback to a World War I military requirement to make students fit for military service--yes, it is still in effect at many schools).
Extracurricular activities span the gamut from Drama clubs to Math societies to Future Farmers of America (FFA). There are dozens of activities and students are often encouraged to get involved. In fact, a student with perfect grades and perfect college exams would still have a problem getting into a top US university if they do not have significant extra-curricular activities.
Parental involvement is considered almost a 'duty' in some school districts. You will be expected to pitch in and volunteer your time to help the school and your kids. At some schools they have an 'auction' where they auction off silly things and expect parents to bid (overbid) with the proceeds going to fund certain school functions. At other schools (many) parents are asked to donate 'a day or two' as a chaperone for a field trip or as a 'teacher's assistant' or just to come in and tell a story during 'What my Mom/Dad does at Work' day. The level of expectation will vary, and drop off as your child moves out of primary and into secondary school. We had a discussion as to whether it was more / less than is expected in the UK, and like most things, the answer was "it varies".
Formal organizations like the Parent-Teachers Association (Organization) exist in most cities with parents having direct contact with school administrators and going over concerns and developments in the school. In some districts, the PTA's are quite active and strong, in effect acting like a 'board of directors' over the school district. In others they are basically non-existent. Many athletic 'booster clubs' also exist to help fund the athletic expenses of the school, such as the sports that do not generate revenue (i.e. no revenue or ticket sales to a high school track meet so boosters donate funds to help run the team).