How do you marry girlfriend in US on tourist visa?

They have to become citizens of that country to marry that person.

As long as she came to the US legally, and has proofnoprior marriage (proof of divorce) you can marry her in the US or her home country. It would be easier to marry her in the US and apply for I-485 status adjustment. They do not have to be a citizen of the country as stated above. You should still consult an Immigration lawyer. Unless you are on the tourist visa, then rolls simply change. You need to file for I-485, and your US citizen spouse needs affidavit of support and other forms of documents.