It is about 8 km from Belarus Station, the Moscow terminus for trains to/from Belarus (Minsk and Brest), Kaliningrad, Smolensk and international destinations including Vilnius, Warsaw, and Berlin, to the Molodyozhny Hotel in Moscow.
By taxi
Depending on the time of day, the journey by taxi will take from 20 to 30 minutes, but should not cost more than $20. If you prefer, you can pre-order a transfer with a driver to meet your train here.
By metro
From Belorusskaya Metro Station (connected to the station concourse), take the brown circle line and travel clockwise one stop to Novoslobodskaya. Change to the gray line and go three stops north to Timiryazevskaya, which is around 500m from the Molodyozhny Hotel.