Kursk Station, 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 a little less than 15 km from the Molodyozhny Hotel.
By taxi
The drive to the Molodyozhny Hotel from the station will take around 30 minutes in reasonable traffic but could be much more at peak times. Taxis should cost $20-30, or to save trouble negotiating on arrival you can book a transfer with driver to meet your train here.
By metro
From Kurskaya Metro Station, which is connected to the concourse of the mainline station, travel three stops counterclockwise to Novoslobodskaya on the brown circle line and then change to the gray line and go north three stops. Get off at the Timiryazevskaya metro station, which is about seven minutes' walk down the road from the Molodyozhny.