By taxi
Official airport taxis from Domodedovo cost around $50 (for an economy sedan) or $70 (for an executive-class car) to downtown Moscow. You can also order an airport transfer with a driver to meet you at the airport here. The journey will take upwards of 90 minutes, depending on traffic.
By train
The Aeroexpress rail link is probably the fastest way to reach central Moscow. Trains run from Domodedovo to Pavelets Railway Station in central Moscow. Trains run daily from 6am to 12am at half-hour intervals, and the journey takes 40-50 minutes. Adult single tickets cost a little over $10 one-way, and there are discounts for children, family tickets and first class tickets also available. To complete the journey, take the metro from Paveletskaya Metro Station, and travel north on the dark-green line two stops to Teatralnaya Metro Station, which is less than five minutes' walk from the Ritz Carlton.
By bus
The only reason to take the bus from Domodedovo is that there are some services running through the night. Nonetheless, they will only take you as far as Domodedovskaya Metro Station in the far south-west of Moscow, and outside metro working hours (roughly from 6am to 12am), it will still require a long taxi ride to reach the Ritz Carlton Hotel.