Kursk Station is the Moscow terminal for trains to/from central Russia (Kursk and Nizhny Novgorod), eastern Ukraine (Donetsk and Kharkiv), and some Sapsan high-speed services from St. Petersburg. It is about 3 km by road from the Belgrade Hotel.
By taxi
The drive to the Belgrade from the station will take about 20 minutes in reasonable traffic, or much more at peak times. Taxis should cost $20-25, or to save trouble you can book a transfer with driver to meet your train here.
By metro
From Kurskaya Metro Station, which is connected to the concourse of the mainline station, take the dark-blue Arbatsko-Pokrovskaya Line three stops west to Smolenskaya. From there it is a short walking distance to the hotel (10 minutes)