if you want to go from Domodedovo airport to the centre of Moscow, there are many variants. The easiest might be the Aeroexpress train, but that costs 420 RUR if you book online and 470 RUR if you buy your ticket at a ticket desk or machine.
If you are on a budget and want to save some money, I recommend you to catch a bus or Mashrutka to Domodedovskaya metro station, from where you can reach the centre within 20mins.
The best of the bus is, that there are many departures every hour and you only need to pay 100 RUR directly to the driver.
Here you find the latest Moscow Metro map and also news about eventual closures of stations: