Kiev Station, the Moscow terminal for trains to/from Kiev and several other European cities including Belgrade, Zagreb, Bucharest, Budapest, Prague, Vienna, and Venice, is a very short metro or taxi ride from the Arbat Hotel, and even within walking distance (about 1km) provided you don't have heavy luggage.
By taxi
The drive to the Arbat Hotel should not take more than ten minutes, and taxis at the station can be negotiated for around $15. It is also possible to order a transfer with a driver to meet your train here.
By metro
From Kievskaya Metro Station (accessed from the mainline station concourse) travel east on the dark-blue line one stop to Smolenskaya, which is roughly five minutes' walk from the Arbat Hotel.
