If you are arriving in Moscow from St. Petersburg, you will almost certainly arrive at Leningrad Station (and also from Helsinki, Tallinn and the Russian North), while Trans-Siberian trains and many other Siberian services arrive at Yaroslavl Station. Kazan Station, meanwhile, serves trains from Central Asia, Western Siberia, the Volga Region, and Southern Russia. All three stations are situated on Komsomolskaya Ploshchad, a square around 6km to the north of the Swissotel Krasnye Holmy.
By taxi
If you are willing to negotiate a taxi at the station on your arrival, the correct price for the journey should not be more than $30. However, it is probably easier to book a transfer with a driver to meet your train in advance, which you can do here. The drive to the Swissotel should take around 30 minutes.
By metro
Take the brown circle line from Komsomolskaya Metro Station, accessed from all three mainline stations, and travel clockwise three stops to Paveletskaya, which is less than ten minutes' walk from the Swissotel.