How do I marry and get a green card for my girlfriend?

It really all depends on how she entered the US and if anyone had ever petitioned on her behalf. If she entered lawfully but overstayed and she is married to a US citizen, she will be able to legalize her status in the US without leaving. If she entered the US unlawfully and is not protected by a previous Section 245i filing, under the current immigration laws, she is not eligible to adjust status within the US. She would have to depart the US but by doing so she would automatically trigger a 10 year bar to reentry, which can only be waived by a showing of extreme hardship to a US citizen spouse and this is fairly difficult to do in most cases.

If someone resides in the U.S. undocumented, she can adjust by marrying a citizen if she entered the U.S. lawfully or if she was a beneficiary of a family or labor petition filed on or before 4/30/01.

Your chances are good as long as you are a U.S. citizen and she entered the U.S. with a visa (such as a B-2 tourist visa) and has proof of her entry, either a stamp in her passport or an I-94 (small white entry card). You get married and file a number of different forms (usually 6 or 7) and copies of the required documents. The forms can be found at the CIS (Citizenship & Immigration Services) website (www.uscis.gov) The instructions for each form tell you what documents you need. You will need to submit copies of your most recent tax return and do an affidavit of support for her (one of the forms). If she entered without a visa, she is probably out of luck unless a petition or application was filed for her in the past (or for a parent when she was under 21).