A foreign citizen must register with the local migration authorities within 7 business days upon arrival. Then a visa has to be re-registered at each city where you stay more than 7 business days.
The registration must be completed by the receiving entity. Please note that the receiving entity is not necessarily the same as the inviting organization or hotel entered in the person’s invitation and visa but a company, hotel or person a foreigner is actually visiting in Russia.
If you do stay at a hotel, the registration is fully taken care of by the hotel reception.
If you stay at a private apartment, your visa is to be registered by your landlord. Please have the landlord apply at the local police precinct (in Moscow) or FMS office (commonly known as OVIR) in other cities. He will just need to fill out a registration form indicating your passport and migration card details. Your landlord will have to present his passport with the registration (a so-called “propiska”) at the same address.