Kursk Station is the Moscow terminal from central Russia (Kursk and Nizhny Novgorod), eastern Ukraine (Donetsk and Kharkiv), and St. Petersburg (some Sapsan high-speed rail link services). It is a little under 8km by road from the station to the Radisson Royal Hotel.
By taxi
It should take 20-30 minutes to reach the hotel by taxi, and you should expect to pay around $25 if you negotiate a taxi on arrival. It is probably easier, however, to arrange transfer with a driver to meet your train, which you can do here.
By metro
The mainline station is connected to Kurskaya Metro Station. From there, take the dark-blue line and travel west four stops to Kievskaya, which is around 400m from the hotel.