It depends on for how long you have had a green card. I think you will be eligible to apply for naturalization after 5 years after obtaining a green card, 3 years if you are married to an American citizen. INS may have changed the rules in the recent years, this is how it used to work. As to how long does it take to actually get through the naturalization once you apply, it varies from state to state. In CA for eg, it may take up to 2 years due to a number of applicants but in midwest it is faster.