Travel, Transit and Cars in America
Yea, you got by being carbon neutral in London living between 5 tube stops and 10 bus lines and a rail network, but the US isn't London, and even in the best cities for public transit like NY and DC you'll quickly find that a car is kind of a nice thing to have.
In small towns and suburbs, it is essential. As important as a roof over your head, a passport, and a telephone.
America is built around the car. Roads, neighborhoods, zoning (planning commission) regulations, stores and work are all focused around someone 'driving' to do these things. With the exception of a few major cities (New York, San Fran, Boston etc) owning and driving a car is *required* to do even the simplest of tasks, such as buy groceries or go out to dinner. Driving the kids to a soccer game two miles away or a birthday party across town is just part of life in America. There is no bus option to take the kids to the movies.
There is important statistic that you should consider--population density. The United Kingdom ranks 50th in population density, with 246 people per sq. km. The United States is 177, with ~36 per sq km (not counting Alaska). That means if there is one grocery store for every 1000 people, then you have one somewhere inside 5 sq km of space in the UK and nearly 30 sq km for the US! Of course this varies by towns and regions (NY is pretty packed) but in a general sense, you need to realize that it is a hike to get the basics of life, a hike that is usually going to require a car.
A common theme behind threads like 'I don't have any friends' and 'I'm so homesick' is the fact that the person is relatively tied to their houses without any means of travel. Either they live in a suburb with only a few sidewalks (pavements) or in a place that simply isn't safe to walk down the street for fear of being run over.
Seriously--budget for a car. Budget for two cars if one is going to be out of service (i.e. at work with the spouse).
Rules of the Road:
There are some differences between the US and the UK relating to driving laws. It is worth noting that many laws regarding driving are state-based and as such you can see different rules and requirements every time you cross a state border. A few things to watch out for would include:
America is huge. To fly from one coast to the other takes a minimum of 6 hours. To drive from one end to the other is measured in days, maybe a week. Trains take almost as long and buses (coaches) are equally slow.
By and large, if you want to get from city to city, you're looking at flying. Four hour drives are about the limit before people start to look at flying as an alternative. On the East Coast (Washington-Baltimore-Philadelphia-New York-Boston) rail is a real option, but in most other places trains are frightfully slow and the distances vast such that it is not a real alternative. A 2 hour flight from NY to Chicago is a 14 hour rail journey, and even then, you are only about 1/4 of the way across the US!
With the exception of big cities, public transportation is very limited in the US. While many smaller communities have buses or light rail, these are often much slower than driving yourself or are of such limited scheduling that using them is incredibly inconvenient. In rural areas there is simply no public transit, or if there is it's often referred to as the 'DUI Wagon' as the only people who use it are those who lost their license due to driving while intoxicated.
In some major cities there are 'Zip' cars, which are car-sharing rent by the hour options for vehicles. By and large this is in major cities where you can get by 6 days a week without a car (but want one on the weekend to run an errand or buy some groceries).