What are the requirements to marry an immigrant

A preacher and a marriage license.

Getting married is not the real issue as much as their legal status to be in the US and then after you marry applying for citizenship. So are you more concerned over their citizenship status,

As for as getting married, just a marriage license and the preacher

You both need 2 forms of IDs, one with photo.
Getting married is not a big deal... to obtain legal status in US is.

If your spouse maintain legal status until you get married, then you should file I-130 (Petition for Alien Relative) to USCIS, when you get an approval then you can file I-485 (Application to Adjust Status). Forms can be downloaded here.

If your spouse has overstayed the visa, or entered US without inspection, you need an experienced immigration attorney to take care of your case.

Good luck..