Marrying a non us citizen in the US is not much different from a Citizen. The process is exactly the same..you apply for a license and have some sort of officiated ceremony by an authorized person( Judge, clergy, JOP..) and have the marriage recorded on the official county record..the key difference with a non us citizen is the some time requirement of a Social security number...the official rule is that IF you have a SSN, you must put it on application...some jurisdiction intrepret this is that you MUST HAVE a SSN to marry, and some intrepret it correctly that you DO NOT have to have a SSN, just must report it if you do. You need to find a county/state where they dont require it. Be specific when you ask because the simple question "do I need a ssn to get a license" will almost always get a yes...specically state you are marrying a non us citizen who does not have a SSN, can you still get a license. Start with your local area, then call around if they do not. Here is a link to the county clerks offices in Vermont..
http://usmarriagelaws.com/search/uni...shtml#counties
Just for Refernce, Franklin county Ohio (Columbus) will issue a license without a SSN.
Once you marry, then it you have to go through the process of adjusting her status to a legal permanant resident (Green card)...here is a link to that process.
http://www.uscis.gov/portal/site/usc...0045f3d6a1RCRD

