Kursk Station is the Moscow terminal for trains from central Russia (Kursk and Nizhny Novgorod), eastern Ukraine (Donetsk and Kharkiv), and St. Petersburg (some Sapsan high-speed services). The station is to the north-east of central Moscow, a little over 3km from the Alrosa Na Kazachyem Hotel.
By taxi
It should not take much more than 20 minutes to reach the Alrosa Na Kazachyem Hotel by car. If you are willing to negotiate a taxi on arrival, the ride should cost no more than $20, but it is probably easier to book a transfer with a driver to meet your train here.
By metro
From Kurskaya Metro Station (attached to the mainline station), take the dark-blue line and travel west two stops to Arbatskaya. Change there to the gray line and travel south one stop to Polyanka, which is around ten minutes' walk from the hotel.