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 a little less than 25 km from the Tsaritsyno Hotel.
By taxi
The drive to the Tsaritsyno Hotel from the station will take around 30 minutes in reasonable traffic but will be significantly more at peak times. Taxis should cost around $30, or to save trouble 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, go two stops clockwise on the brown circle line to Paveletskaya and from there change to the dark-green line and travel six stops to Orekhovo. It is a ten minute walk to the Tsaritsyno Hotel from the metro station.
