Naturalization US Citizenship Resources
Please read the above page for the basics regarding how long you must live in the US as a Permanent Resident and the other conditions you must meet before lodging your application. In general, you must be a US Permanent Resident for five years before you can become a US citizen.
You may apply in the 90 days before you become eligible; IE: if you will have your 5th anniversary as a Permanent Resident (Green Card) on March 15, 2008 and you otherwise qualify, you could submit your application as early as December 16, 2007. Use a 'date calculator' like this one to make sure you do not apply too early.
 Naturalization: Waivers, Exceptions, and Special Cases
Family Members of U.S. Citizens, Spouses of U.S. Citizens Waiver for Spouses: 3 years instead of 5
In general, if you have been a Permanent Resident for three years and have been married to and living in a valid marital union with the same U.S. citizen spouse for all three years AND you meet the other criteria (Residence and Physical Presence, Good Moral Character, Language etc), you are eligible for naturalization.
So called "Conditional Permanent Residents" are Permanent Residents nonetheless.
 When does my time as a Permanent Resident begin?
Your time as a Permanent Resident begins on the date you were granted permanent resident status. This date is on your Permanent Resident Card (formerly known as Alien Registration Card) aka your Green Card.
 Physical Presence Is Important!
An applicant is eligible to file if, immediately preceding the filing of the application, he or she:
Note: There is an interplay between absences between six months and one year. Once a person is out six months, there is a "presumption" that continuity of residence was broken. However, this presumption can rebutted by proof that there was no intent to abandon residence. The modicum of proof to rebut the presumption varies by the individual facts; e.g. an absence of six months two days will be easy to rebut. In addition, practice can vary between location in the US or even between individual USCIS examiners. Once, a person has been out a year, the presumption then becomes conclusive -- the reason for the absence does not matter.
TIP: this discussion is about "continuity" of residence. Assuming that residence was not abandoned, the continuity "clock" is reset to 364 days upon return to the US. For example, Ms. Green-card travels outside the US and is abroad for one year three months, she will have 364 days of continuous residence upon return presuming she did not abandon status in the US.
Further tip: This is one which should be avoided unless absolutely necessary -- one is considered to be maintaining residence for any day where any part of the day is physically in the United States. This includes both the day of departure and the day of return. For example, assume a person departs on January 1st and returns the following January 1st. Other than a leap year, there has been an absence of only 364 days, not 365. However, this is a very subtle point which will be missed by USCIS examiners absent vigorous legal representation. If this makes for a short delay in application, it is advisable to wait.
(for spouses of US Citizens filing under the "3 year" exception rule, change all "5 year" notes to 3 years, and note that the physical presence requirement changes from 30 months in 5 years, to 18 months in 3 years)
From the day you become a Permanent Resident, start keeping track of ALL dates spent out of the USA, including departure and return dates of travel. This is true for both business or leisure travel. Keep this list in one place, where it is easy for you to get at, and it will make completing N-400 much, much easier! This is an especially good idea for Canadians who cross the border a lot. Everyone should save whatever travel documentation available should it be required.
Study materials in many languages, Flash Cards and test questions: Civics and Citizenship Study Materials
 A MUST read:
Dual Citizenship FAQ Dual Nationality and United States Law by Rich Wales
Read here before you swear: Oath of Allegiance for Naturalized Citizens