Trains arrive at Belarus Station from Belarus (Minsk and Brest), Kaliningrad, Smolensk and international destinations including Vilnius, Warsaw, and Berlin. The station is around 15 km north of the Korston Moscow Hotel.
By taxi
It should not take more than an hour to drive to the Korston Moscow Hotel except in the worst rush hour traffic. If you can negotiate a taxi on arrival, the fare should be around $40, but it is probably easier to arrange a transfer with a driver to meet your train, which you can do here.
By metro
If you would prefer to use public transport, take the dark-green line from Belorusskaya Metro Station and travel three stops south to Teatralnaya. Change there to the red line and continue six stops south to Vorobyovy Gory, which is 500m from the Korston Moscow Hotel.