The international airports connecting Moscow are Domodedovo, Vnukovo and Sheremetyevo. After reaching any of the Moscow airports from abroad, you can take aero express train or taxi service to reach the city. If you are flying inland, you can go for domestic flights or take Russian Railway to reach Moscow.
There is also good metro service that operates in major Russian cities. You may want to consult a Moscow tourism guide before deciding the best and cheap mode of travel for you.