To get married in Russia, you need to prove to the authorities you are who you say you are, and that you are free to marry. To do this you provide your passport (to show who you are), a certificate of non-impediment and if necessary your divorce certificate (to show you are free to marry).
Can I marry Russian?
You can also choose to get married first in Russia or another country, and then apply for an immigrant visa with which to enter the United States. That means your spouse can obtain permanent residence in the U.S. only after a visa number (space for another permanent resident) has become available.
How can a foreigner get married in Russia?
To get married in Russia, you need to prove to the authorities you are who you say you are, and that you are free to marry. To do this you provide your passport (to show who you are), a certificate of non-impediment and if necessary your divorce certificate (to show you are free to marry).