Kursk Station is the Moscow terminal for trains arriving from central Russia (Kursk and Nizhny Novgorod), eastern Ukraine (Donetsk and Kharkiv), and some Sapsan high-speed services from St. Petersburg. The station is around 4km east of the Ritz Carlton Hotel.
By taxi
If you take a taxi to the hotel, the drive will take around 20 minutes in reasonable traffic. Taxis should cost $15-20, but if you don't wish to negotiate with drivers at the station it is probably safer to book a transfer, which you can do here.
By metro
From Kurskaya Metro Station (linked to the mainline station) take the dark-blue line and travel one stop east to Ploshchad Revolyutsii, which is around five minutes' walk from the Ritz Carlton Hotel.