The three stations on Komsomolskaya Ploshchad (around 10km from the Historical Hotel Sovietsky) welcome trains from St. Petersburg, Helsinki, and Tallinn, Central Asia and Siberia, and numerous cities in European Russia.
By taxi
It should take no more than 30 minutes to reach the hotel by road. If you are prepared to negotiate with a driver at the station, you should not be paying more than about $30 for the trip, but it is probably safer and easier to book a transfer with a driver to meet your train, which you can do here.
By metro
Komsomolskaya Metro Station is connected to all three mainline stations. From there, take the brown circle line and travel anticlockwise three stops to Belorusskaya. Change to the dark-green line and continue north one stop to Dinamo, which is roughly 500m from the Historical Hotel Sovietsky.