It is about 25 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 Soyuz Hotel.
By taxi
Depending on the time of day, the journey by taxi will take from 30 to 60 minutes, but should not cost more than $40. 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 mainline station concourse), take the dark-green line and travel north six stops to Rechnoy Vokzal. From there, take the 138 or 739 bus, and it is a ten-minute ride to the Soyuz Hotel, which has its own bus stop.