By taxi
The drive from Domodedovo to the hotel is unlikely to take much less than 90 minutes. Official airport taxis cost roughly $50 (for an economy-class sedan) or $70 (for executive class sedans and MPVs). You can arrange a transfer with a driver to meet you off the plane here.
By train
Aeroexpress trains run from Domodedovo to Pavelets Station in downtown Moscow. Services operate daily at 30-minute intervals from 6am to 12am. The journey takes 40-50 minutes and standard adult single tickets costs a little over $10, with child discounts, family tickets, and first-class tickets available. From Paveletskaya Metro Station, take the dark-green line and travel north six stops to Dinamo, which is around 500m from the hotel.
By bus
There are bus services from Domodedovo to Domodedovskaya Metro Station, in the south-east of Moscow. The only reason to use bus is if you are arriving late at night and wish to save money on taxis (although bear in mind that the metro only runs between 5.40am and 1am). The marshrutka minibus shuttle service costs $4-5 and runs from 6am to 12am every 15 minutes, with a less frequent service all through the night. From Domodedovskaya, it is 13 stops north on the dark-green line north to Dinamo Metro Station, approximately ten minutes' walk from the Renaissance Moscow Monarch Centre.
