Kursk Station is the Moscow terminal for rail services from central Russia (Kursk and Nizhny Novgorod), eastern Ukraine (Donetsk and Kharkiv), and St. Petersburg (some Sapsan high-speed services). It is just under 15km to the Art Hotel from the station.
By taxi
If you are ready to negotiate a cab on arrival, you should try to pay not much more than $40 to reach the Art Hotel. It may, however, be safer to book a transfer with a driver to meet you off the train, which you can do here.
By metro
From Kurskaya Metro Station, connected to the mainline station, take the dark-blue line and travel west one stop to Ploshchad Revolyutsii. Change to the dark-green line from Teatralnaya and travel north six stops to Sokol. From there, it is a little less than 1km on foot to the Art Hotel.