These three mainline stations, where trains arrive from St. Petersburg, Tallinn, Helsinki, Central Asia, Vladivostok, and Beijing, are located on Komsomolskaya Ploshchad, a little over 7km by road from the Arbat Hotel.
By taxi
If you plan to negotiate a taxi on arrival, you should not pay more than $25 for the trip to the Arbat Hotel. However, it may be easier to book a transfer with a driver to meet you off the train, which you can do here. The drive to the hotel should take around 20 minutes.
By metro
Komsomolskaya Metro Station is connected to all three stations. Take the brown circle line and travel clockwise one stop to Kurskaya. Change there to the dark-blue line and head west three stops to Smolenskaya, which is around 200m from the Arbat Hotel.