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 south of the Altay Hotel.
By taxi
It should not take more than 30 minutes to drive to the Altay Hotel except in the worst rush hour traffic. If you can negotiate a taxi on arrival, the fare should be around $30, 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 prefer to use public transport, take the brown circle line from Belarusskaya Station and travel one stop clockwise to Novoslobodskaya. Change there to the gray line, and continue five stops north to Vladykino, which is just over five minutes' walk from the Altay Hotel.