The best thing for you and your girlfriend to do would be to consult with a licensed, experienced immigration attorney who can verify your eligibility and whether you potentially may have any inadmissibility issues that would affect your marriage-based residency petition, as well as provide an overview of the application process. Although the process may seem straight-forward, there are several forms, various supporting documents, and even seemingly innocent questions on the forms that can cause complications, delays and even denial and instigation of removal (deportation) proceedings before the Immigration Court if everything is not completed and submitted correctly.
However, should you wish to get an overview of the process yourselves, you may wish to start with the U.S. Citizenship and Immigration Service website, www.uscis.gov. Under the "green card" heading on the main page, look at "green card through family" and then "immediate relative" links.
For assistance locating licensed, experienced immigration attorneys for a consultation, you can look here on Avvo, at www.aila.org or www.immigrationlawhelp.org. Keep in mind that you are not under any obligation to hire an attorney simply because you consulted with him/her.