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