Kursk Station, which is located just over 2km north-east of the Swissotel Krasnye Holmy, is the Moscow terminal for trains from central Russia (Kursk and Nizhny Novgorod), eastern Ukraine (Donetsk and Kharkiv), and some services from St. Petersburg (including some Sapsan high-speed services).
By taxi
It will take 15-20 minutes to reach the Swissotel Krasny Holmy by car from the station, and you can book a transfer with a driver to meet your train here. If you are willing to risk negotiating a taxi on arrival, you should try to pay no more than $20.
By metro
From Kurskaya Metro Station, which is connected to the mainline station, take the brown circle line and travel clockwise two stops to Paveletskaya, which is less than ten minutes' walk from the hotel.