Getting There and Away: Moscow Russia
Info now taken from Lonely Planet website, as it is very useful and good info here it is:
If you’re coming in from an overseas flight, Sheremetevo-2 is the airport you’ll fly into; there are also four airports to handle travel to domestic destinations and the ex-Soviet states. There’s a network of comfy-enough buses that run to places within about a 700km (435mi) radius of Moscow. The city also has 9 main rail stations, and you can jump on trains to most parts of Russia and Europe as well as China and Mongolia.
Sheremetevo-2 airport, 30km (20mi) northwest of the city centre, handles flights to and from places outside the former Soviet Union. There are daily flights by numerous airlines to and from nearly all European and many other world capitals, and many provincial cities, too. A flight from London or Paris takes about three hours, from New York about 10 hours. Four Moscow airports are devoted to flights to and from places within Russia and the other ex-Soviet states. Check-in for flights within the ex-USSR is supposed to close 40 minutes before take-off, but be sure to reach the airport well before that.
International flights from most Moscow airports incur a departure tax which is included in the price of airfares. You can get to all five airports and the city centre cheaply by a combination of bus and metro or suburban train, but if you’re going early in the morning or late at night, or have a lot of baggage, you’ll probably need a taxi. The easiest approach is to arrange an airport-city transfer through a travel agent; you’ll pay no more than an average taxi fare.

Moscow has rail links to most parts of Russia, most former Soviet states, numerous countries in Eastern and Western Europe, and China and Mongolia. Moscow has nine main train stations, all with metro stations on the spot.
Buses run to a number of towns and cities within about 700km (435mi) of Moscow. Buses are reasonably comfortable but to most places they’re a bit slower than trains, and less frequent.
Website: http://www.lonelyplanet.com/destinations/europe/moscow/get.htm