Trains arrive at Belarus Station from Belarus (Minsk and Brest), Kaliningrad, Smolensk and international destinations including Vilnius, Warsaw, and Berlin. The station is around 4 km north of the Arbat Hotel.
By taxi
It should not take more than 20 minutes to drive to the Arbat Hotel except in the worst rush hour traffic. If you can negotiate a taxi on arrival, the fare should be around $20, 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 Belorusskaya Metro Station and travel two stops anticlockwise to Kievskaya. Change there to the dark-blue line and continue one stop east to Smolenskaya, which is around 200m from the Arbat Hotel.