On arrival in the airport, you have to fill in a migration card before going through passport control. Keep this paper with you during al your staying in Russia, because you'll need it:

• visiting other cities in Russia
• deparing from russia you must show your migration card to the custom's officer

Coming to any russian city you should be registered. You can be easily registered it the hotel,you're staying at, or, in the Passport and visas Department of Ministry of Internal Affairs (PVU). You must be registered in 72 hours after your arrival. 

• If you are staying at a hotel in Russia, you can be registered at the front desk. You will be asked for your visa and passport. A small registration fee may be imposed. The registration is made for the period of your accommodation in the hotel.
• If you are staying by your friends, relatives or in your own flat, you can be registered in  PVU. It is a bit more complicated procedure, than registering in a hotel.