The easiest, and best way to get around Moscow is by using the fantastic Metro system.
One of the real treasures of the communist era, Moscow's Metro carries more passengers a day than New York and London's combined, and the stations are works of art in their own right, architectural masterpieces deep underground, with mosaics and murals depicting the eternal struggle of the worker. The Metro is good value - if a little busy, but it does serve the whole city, so you can get practically anywhere you might want to go.
Taxis in Moscow are an option, as are limousines for a special night out, although you probably wouldn't want to drive in the city, hiring a car is a good option if you plan to leave.
The Trans Siberian Railway originates in Moscow, and takes passengers all the way into the Far East on a weeklong 9500KM journey, should you fancy a trip.
