After you arrive to Russia
You bring the visa with you when you fly to Russia and present it at immigration at the airport (they stamp it).
Important: All foreigners are given migration cards upon their arrival to Russia.
The card - actually a narrow slip of paper divided into two identical parts - contains personal details such as name, date of birth, passport number and citizenship and the planned length and purpose of the foreigner's stay in Russia. Both halves are filled out at the point of entry into Russia. Part A is surrendered on entry and part B on departure. Part A of the migration card will be taken by passport control upon arrival, and part B will be taken when leaving the country. Part B should have a visa registration stamp.
The cards will be used to form a national database of how many foreigners are in the country.
Within three days of your arrival in Russia, you need to register your visa. This registration is normally done at most hotels.
Russian law requires that you register your visa within 3 working days of your arrival in Russia.
This is important, and fines are levied by policemen conducting a document check, travel tickets can be hard to purchase within Russia; and the worst of all, having problems at passport control when leaving the country are the major pitfalls of non-registration. Some people who have not registered have been lucky, and not penalised, but these are few and far between.
If you are staying in a flat, then you should have a special letter from the person whose flat it is, and they will be responsible for registering you with the UVIR (the Passports and Visas Department). These are the ones who generally fail to register because of the complexities.
Travelling on a tourist visa, a hotel will register you.
Businessmen travelling on a business visa will again be registered by the hotel they stay in, alternatively the company inviting them could register them at the place of issue of the invitation.