By taxi
If you are traveling to the Sheraton Palace from Domodedovo by car, the drive will take around 90 minutes (or more at peak times). Official airport taxis cost roughly $50 or $70 depending on the type of car. If you prefer a driver to meet your flight, you can arrange a transfer here.
By train
Aeroexpress trains run from the airport station daily at 30-minute intervals from 6am to 12am to Pavelets Station in downtown Moscow. It's a 40-50 minute journey, and standard adult single tickets costs a little over $10, with child discounts, family tickets, and first-class tickets available. Then, take the metro from Paveletskaya Metro Station and travel north five stops on the dark-green line to Belorusskaya, which is around five minutes' walk to the hotel.
By bus
Bus services run from Domodedovo to Domodedovskaya Metro Station in the far south-east of Moscow. From the bus stop between exits 2 and 3 of the arrivals lounge, regular buses ($3-4, from 6am to 12am daily every 15 minutes) take 25-30 minutes to reach the metro, while the marshrutka minibus shuttle service ($4-5, from 6am to 12am every 15 minutes, and with a less frequent service all through the night) is slightly quicker. Then, take the metro from Domodedovskaya and travel north on the dark-green line five stops to Belorusskaya, which is about 300m from the Sheraton Palace.