When you arrive at the Russian border (at the airport, or at a land border, depending on how you travel to Russia) you will have to fill in a migration card. This is a small printed slip of paper that requires a number of details from you.
Once filled in, immigration officials will stamp your migration card, and return it to you. You must ensure you keep it safe and do not lose it, as you need to hand it in when you leave Russia at the end of your trip.
You can see a sample migration card on this page.