Fly into Sheremetyevo Airport (SVO), the closest airport, located 21.1 mi (34 km) from the city centre. If you can't find a flight that's convenient for your trip, you might consider flying into Moscow (VKO-Vnukovo Intl.), which is 8.2 mi (13.2 km) away.
You might consider catching a ride on the metro at Yugo-Zapadnaya Station for ease of access to the rest of the city.