By taxi
It should take around 45 minutes to reach the hotel in clear traffic. Official airport taxis currently cost around $60, or if you prefer you can book an airport transfer to meet your flight here.
By train
Aeroexpress trains will take you from the station at Sheremetyevo (behind Terminals D, E and F, with a free bus connection from Terminal B) to Belarus Rail Station. The service operates daily every 30 minutes from 5am to 12.30am, with a journey time of around 35 minutes. Standard adult tickets cost roughly $11. From Belarus Station, travel two stops counterclockwise on the brown circle line to Kievskaya. Change here to the light-blue line, and continue west four stops to Bagrationovskaya, which is within walking distance of the AST-Hof Hotel.
By bus
There are also buses running from all terminals at the airport to Rechnoy Vokzal Metro Station in the far north of Moscow. Regular buses run from 5.35am to 12.49am, take around 30 minutes to reach the metro, and cost around $1. Be sure to use the 851E service (as opposed to simply 851), to avoid a long journey with several suburban stops. There is also a marshrutka minibus shuttle that runs the same route from 6.45am and 9.45pm, is slightly quicker, and costs a little over $2.