The airport is 29km from the city. You can go by car by the exit motorway (M-10) or it is easy to get to the airport conveniently by:
Taxi (“Autoline” mini-bus taxi)
Express-bus , operating daily at 20 minutes departure interval.
Bus; No 851 from “Rechnoy vokzal” metro station (green line) and No 817 from “Planernaya” metro station (purpe line). Fare is collected on the vehicle. Operating hours: from 5.45 A.M. to 0.30 A.M.
You may get to Domodedovo Airport, 85 kilometers from Sheremetyevo Airport by Taxi (a one hour drive) or by Express-buses (in approximately 111 hours; via City Air Terminal where buses depart every 30 minutes. You may get to Vnukovo Airport by Taxi (50 minutes) or by Express-buses (one hour; via City Air Terminal from where buses depart every 30 minutes. You may get to Bykovo, 70 kilometres from Sheremetyevo Airport by Taxi (50 minute drive) or by Express-buses (one hour drive, via City Air Terminal where buses depart every hour.
Driving is really a headache in Russia, there are restrictions on how far you can travel per day as well as a special "Autotourist" visa to be secured, add to this poor road conditions, lack of petrol stations and lack of emergency roadside help and you'll see why backpackers tend to stick to the rail and bus networks.