How do I go about marrying my non US citizen girlfriend?

You can go to the local court house and get marriage license and then register your marriage, after that you can apply for her to become a Green Card holder

If she is in the US in a different nonimmigrant status, you would get married and after the marriage you can petition for her green card and at the same time she would be able to apply for an adjustment of status from whatever her current status is to permanent residence.

Marry,file your petition and apply for her adjustment of status. If you need help get assistance of a lawyer.

You can marry her just like you would any US citizen. After marriage, you have to work on her adjustment of status. Several forms will have to be filed with the USCIS so that your wife can obtain her conditional green card.

You can marry her and apply for her green card. The forms to be filed are I-485, I-130, G-325A, I-765, I-131, G-28, and I-864. These forms can be found at www.uscis.gov.

If your girlfriend is currently in valid student status (F, J, or M) and entered lawfully you should have no major obstacle to asking her to marry you and proceeding with the filing of the requisite series of concurrent petitions on her behalf for adjustment of her status to that of a lawful permanent resident (LPR) as the spouse of a US citizen. You should seek the counsel and guidance of an experienced immigration attorney to help you both through the process. It is more complicated and time-consuming than you would expect and will take between 7 months to a year to complete. Additionally, there are important legal considerations for removal of the conditions on residence for your alien spouse at the conclusion of the conditional residency period (first two years of your marriage) which you will need to consider.