Kursk Station is the Moscow terminal for intercity trains from central Russia (Kursk and Nizhny Novgorod), eastern Ukraine (Donetsk and Kharkiv), and the Sapsan high-speed train from St. Petersburg. The station is about 3km east of the Baltschug Kempinski Hotel.
By taxi
If you take a taxi from Kursk Station to the Baltschug Kempinski Hotel, it should take around 15 minutes (or much more at peak times) and cost $15-20, or you can order a transfer to meet your train here.
By metro
From Kurskaya Metro Station, which is connected to the mainline station, take the dark-blue line one stop west to Ploshchad Revolyutsii. Change there to the dark-green line and conrinue one stop south to Novokuznetskaya, which is just under 15 minutes' walk from the Baltschug Kempinski Hotel.