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 to/from St. Petersburg. It is located around 4km from the Marriott Grand Hotel to the south-east.
By taxi
It should take around 20 minutes to reach the Marriott Grand by taxi (but can take much longer at peak times), and taxis will cost $20-$25. You can also order a transfer with driver to meet you off your train here.
By metro
Take the metro from Kurskaya Metro Station, which is accessed from the concourse of the mainline station, and travel west on the dark-blue line one stop to Ploshchad Revolyutsii. Change to the dark-green line and travel north two stops to Mayakovskaya, which is on the same block as the Marriott Grand.