As you exit customs to the main floor of Sheremetyevo 2, you'll be greeted by a barrage of annoying, pushy taxi drivers who want very badly to charge you around $50+ dollars to take you to your destination. There's a much cheaper route to go, though, and you'll be able to get to almost any main hotel in Moscow.
Before you leave for a trip for Moscow, make sure you get a map of the metro, either from a travel book or online.
First, don't even make eye contact with the taxi drivers or say anything to them. Don't even say "nyet" or they will begin to follow you.
Second, exchange some money at the airport. The exchange rate is not the best, but it will help you get started.
Third, go out of the main doors and look for some vans that are obviously designed to carry passengers. These are the "Marshutka" vans. Some go to Sheremetyevo 1, and some go to "Rechnoi Vockzal." You'll want the one for "Rechnoi Vockzal." If you don't speak Russian, just stick your head in a van and say "Rechnoi Vockzal" with an inquisitive tone. You should either get a "da" or a "nyet" (yes or no). When the van is full, the van will go. The drive to Rechnoi Vockzal is about 30 minutes.
The marshutka as of February 2005 was only 25 rubles. If you have extra luggage, the driver may ask you to pay for an extra seat, but this has never happened to me with one suitcase and a small shoulder bag. It is a little cramped at times, though.
Rechnoi Vockzal is a main metro stop. As you enter the doors, you should see a desk where you can buy metro rides. As of February 2005, five rides were 60 rubles. Again, if you don't speak Russia just walk up to the window and hold up 5 fingers while handing the person money. You'll receive a card that you'll insert through the machines that lead to the escalators.
If you have luggage, look for person sitting in the booth by the card machines. Simply walk up to the booth. She will motion to you how many times you will need to put the card through for both you and your luggage. This can be done without speaking.
From this point on, use your metro map to figure out where you want to go.
MAJOR TIP: Before you visit Russia, take an hour one afternoon to learn the Cyrilic Alphabet. It is not hard, and it will make your trip to Moscow much easier. Your metro map from a travel book may use Latin characters, but the signs in the metros still do not. You'll fare much better if you can at least sound out the words.