When you arrive in Moscow, shuttle trains are the easiest and fastest way to get to the city centre. Shuttle trains depart from each airport every 30 minutes. When you arrive at the airport, look for the sign "Train to Moscow", which will lead you directly to the train station.
Another option is going by taxi. The trip may be longer due to traffic jams. If you prefer to go by taxi, make sure you use a reliable taxi service: there is a taxi counter in each airport terminal, so go straight to it, tell the agent or driver the address of your hotel and check how much the trip will cost.