By taxi
The drive to the Alrosa Na Kazachyem Hotel from Sheremetyevo takes around 40 minutes in clear traffic, but will more often take at least an hour. Official taxis from the airport currently cost about $60 for the trip, or you can book a transfer with a driver to meet your plane here.
By train
Aeroexpress trains run from the airport station behind terminals D, E and F to Belarus Station in central Moscow. The service operates from 5am to 12.30am daily, with trains every half-hour, and the trip takes 35 minutes. Standard adult tickets currently cost around $11. From Belorusskaya Metro Station (connected to the mainline station), take the dark-green line and travel south two stops to Tverskaya. Change there to the gray line and continue south two stops to Polyanka, which is roughly ten minutes' walk from the Alrosa Na Kazachyem Hotel.
By bus
Buses are considerably slower and less comfortable than the Aeroexpress, and the only reason to consider using them is if you are arriving at terminals B or C (although the former has a free shuttle service to the airport station). The 851 and 851E services run from all terminals at Sheremetyevo from 5.35am to 12.49am to Rechnoy Vokzal Metro Station in the north of the city. The drive takes 30-50 minutes. The 949 shuttle minibus runs the same route from 6.45am and 9.45pm and is slightly quicker. The buses cost around $1, while the minibus costs a little over $2.