Get the number 119 bus right outside the airport terminal, get off at Devjicka. Here you can pick up the underground to the nearest station to your hotel. It is best not to use taxis, they have a bad reputation. You will need to buy tickets to use the buses and trains first otherwise you'll get fined. You need to validate a ticket as you board the relevant transport, can't remember exactly but I think one ticket covers you for an hour or something, do check.
before you leave the airport purchase your tickets, when i last visited a �5 ticket gave me unlinited travel for 7 days. if i remember correctly the ticket office can be found on the ground floor by the exit doors.
have fun
if your drinking you'll find just away from the tourist spots are cheapest, beware of pickpockets and stay safe