Must Know:
Migration card: Upon entering the Russian Federation, you must complete a migration card. If applicable, visitors will be required to indicate their visa information on the migration card. Upon arriving at your destination in the Russian Federation, the migration card should be presented to the host party (hotel, private accommodation owner, etc.)
Visa Registration: All foreign travelers staying in the Russian Federation must be registered with the Federal Migration Service in the city or region where they are staying within seven days of their arrival.
If you are travelling on a tourist visa and staying in a hotel, the registration process is normally completed by reception staff on the first day of your stay, and all that you will need to do is provide them with your passport and migration card The same should be true if you are renting an apartment through an agency. If you are traveling on a business visa, the company inviting you is responsible for registering you, while if you have a private visa, then the Russian citizen who invited you will need to register you. Registration can be completed by them at local branches of the Federal Migration Service or any post office, and again they will need your passport and migration card to complete the process.
If, for whatever reason, your accommodation provider is unwilling to register you (despite their legal obligation) there are always agencies in large cities that will register you for a fee.