DO NOT LET HER LEAVE THE COUNTRY!
If she entered legally and just overstayed, you can get married and petition to adjust her status to permanent residency (green card) WITHOUT her having to leave the country first. If she leaves first, she will be subject to a ten year ban from re-entry.
Here is a link to the USCIS immigration through a family member (Spouse)
http://www.uscis.gov/portal/site/usc...0045f3d6a1RCRD
Overall process takes about 3-4 years...she will get her Conditional permanant residency card within about 6 months-1year. Cost about 3000-6000 depending on whether or not you use a lawyer (highly recommended)
Getting married is not any different that if both were citizens. The only issue is that some jurisdiction "require" a Social security number to obtain a license. Some do, some dont. If your county/state requires, then search around for another county/state that does not.

