By taxi
In good traffic, the trip by taxi will only take about 30 minutes. The cost of an official taxi should be around $50. It is also possible to book an airport transfer to meet you off your flight here.
By train
The 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. This train services has a daily operation schedule of every 30 minutes from 5am to 12.30am, with a journey time of about 35 minutes. Adult tickets will cost you about $11. From Belarus Station, take the metro one stop north on the dark-green line. From Dinamo Metro Station, it is a little under 15 minutes' walk to the Aeropolis Hotel.
By bus
A bus service operates from all terminals of the airport. The buses deliver you to Rechnoy Vokzal Metro Station. The regular bus service operates from 5:35am to 12:49pm and the 30 min ride to the metro will cost about $1. You should make sure to take the 851E service as the 851 will force you to sit through multiple suburban stops. The taxi-bus service (marshrutka) runs the same route at a quicker pace for just over $2 from 6:45am to 9:45pm.
Once you reach the metro station, head south on the dark-green line four stops till you reach Aeroport Station. It is just over ten minutes' walk from there to the Aeropolis Hotel.