Belarus Station is only about 3 kilometers south of the Aeropolis Hotel. It serves as the end point for trains issuing from Belarus (Minsk and Brest), Smolensk, Kaliningrad, Vilnius, Warsaw, and Berlin.
By taxi
Luckily, the Belarus Station is located so close to the Aeropolis Hotel that it will only take 15 minutes or less to get to the hotel except in the absolutely worst rush hour traffic. If you feel bold enough to negotiate with the pool of drivers at the exit of the station, the price you should not go over $15. Nonetheless, it is probably easier and much less stressful to simply book a transfer in advance by using the following link.
By metro
If you prefer to take public transport from the station to the hotel, go one stop north from Belorusskaya Metro Station to Dinamo Station on the dark-green line. From this point it is under 15 minutes on foot to the Aeropolis Hotel.