Filing government forms can be confusing and tedious work, therefore if the following gets confusing... please contact an Immigration Attorney to help you. However, as luck would have it, the Citizenship (Or Naturalization) forms are less confusing than the other immigration forms that need to be filed.
First, go to the website www.uscis.gov and then go to "FORMS" to find the Naturalization papers. The Naturalization papers are labeled "N400″. Print out both the forms and the instructions and any other pamphlets of booklets online that you may want to read up on to help you on this endeavor.
Next, you need to make sure that you meet the requirements to get your Citizenship. Are you a lawful permanent resident (green card)? Have you been one for at least five years? Then you are certainly eligible for the N400 Naturalization. You are also eligible if you are a Lawful permanent resident for atleast 3 years AND married and living with a U.S. Citizen AND your U.S. Citizen spouse has been a Citizen for atleast 3 years. There are a few other ways to be eligible for Naturalization, but these are the main ways green card holders become Citizens.
Then, fill out the form. Make sure to READ EVERYTHING CAREFULLY and use a black ink to fill out paper work. Department of Homeland Security does not suffer mistakes lightly, they will send back your file and make you re-file your whole case for what may you feel to be a small mistake...
Along with filing your forms you will also need to submit evidence. Documents such as copies of your passports, marriage certificates, etc. Make sure that you gather all the evidence and make legible copies! Also, very important to having your form successfully filed.
Finally, the Citizenship interview. If you file everything correctly and there are no issues with your forms and evidence, you will get a notice in the mail scheduling you for an interview at your local Department of Homeland Security office. There are practice citizenship tests that you can obtain to test your knowledge. It is very important that you come to the interview prepared and able to speak English at a conversational level.
Good luck and congratulations because you are on your way to becoming a United States Citizen!