Flying to / from Moscow.

There are three major airports in Moscow: Sheremetyevo, Domodedovo, and Vnukovo. 

If you come from abroad you will arrive either to Sheremetyevo 2 international airport (all major international airlines and Aeroflot) or to Domodedovo international airport (Swiss Airlines, AirMalta, British Airways, Emirates, El Al, China Eastern, Singapore Airlines, Thai Airways and most of the Central Asian airlines, plus most domestic airlines, except Aeroflot).

If you take a domestic flight, it'll be either to / from Sheremetyevo 1 or Domodedovo airports. The new and renovated Vnukovo airport serves mostly domestic flights (UtAir, Vladivostok Avia, flights to North Caucasus), as well as German Wings flights to/from Germany.

Arriving / Departing with a Train.

There are 9 train stations ("vok`zal" in Russian) in Moscow. Each has the name of the main direction for the trains that depart from this railway station. All the railway stations are located close to the center of the city.

The three train stations "Kazanski", "Yaroslavki" and "Leningradski" are located at the same area next to "Komsomolskaya" metro station (north-east center) and that's the stations you will use most likely to go to St. Petersburg or Trans-Siberian.