You have two working options: 1) car or 2) train+metro. Choose the most appropriate option based on your budget and arrival time.
Taxi / Transfer
If you travel in small group (2-4 persons) the car option will be cheaper. The price varies from 1500 to 3000 RUB. You can arrange taxi in advance, or you can take a car from the airport. Don’t take a taxi during rush hours. The most undesirable time is 8-10am and 5-9pm. During this time you will need not less than 2 hours to reach Moscow. And one more advice: don't take a taxi from the guys standing outside of the airport. Find official "booth" and check the price in advance.
Aeroexpress plus Metro
The second option is train+metro. It’s easy to find the station at the airport – just follow the sign “Aeroexpress” or “Trains”. Aeroexpress is a non-stop train. It will arrive to the Belorussky railway station, that is closed to Belorusskaya metro station (green line). Read the article How to use metro in Moscow to get the information regarding metro. There is an option to buy one way Aeroexpress ticket plus one way metro ticket. You can check the schedule and buy tickets online on Aeroexpress website.
And here is a video that may help:
Published on Dec 24, 2017