Kursk Station is the Moscow terminal for trains to/from central Russia (Kursk and Nizhny Novgorod), eastern Ukraine (Donetsk and Kharkiv), and some Sapsan high-speed services from St. Petersburg. It is 3 km from the Tatiana Hotel.
By taxi
The drive to the Tatiana Hotel from the station will take no more than 15 minutes in reasonable traffic, or much more at peak times. Taxis should cost $15-20, or to save trouble you can book a transfer with driver to meet your train here.
By metro
From Kurskaya Metro Station it is two stops clockwise on the brown circle line to Paveletskaya, which is about 300m from the Tatiana Hotel.