By taxi
The journey from Domodedovo to the Derzhavnaya Hotel by car will take around 70 minutes in reasonable traffic. Official airport taxis cost $55-70 (depending on the class of car), or you can arrange a transfer with a driver to meet your flight here.
By train
Aeroexpress trains run from Domodedovo to Pavelets Railway Station. Trains run daily at 30-minute intervals from 6am to 12am, and the journey takes 40-50 minutes. Standard adult singles cost a little over $10, with discounts for small children and family tickets available. Then, from Paveletskaya Metro Station, travel four stops anti-clockwise to Prospekt Mira on the brown circle line. Change here to the orange line, and travel three stops north to VDNKh, which is a little over five minutes' walk from the Derzhavnaya Hotel.
By bus
There are also bus services running from the airport to Domodedovskaya Metro Station, in the far south-east of Moscow. Buses leave the airport from the stop between exits 2 and 3 of the arrivals lounge. There is a choice of regular bus service ($3-4, from 6am to 12am daily every 15 minutes, journey time 25-30 minutes) and a minibus shuttle service ($4-5, from 6am to 12am every 15 minutes, and with a less frequent service all through the night). Take the dark-green line north from Domodedovskaya and travel eight stops to Novokuznetskaya Metro Station. There change to the orange line and travel seven stops north to VDNKh, which is a little over five minutes' walk from the Derzhavnaya Hotel.