Ferenc Liszt International Airport is small, but it has everything you need. It's located about 20 kilometers from the center of Budapest and is divided into three terminals: 1, 2A and 2B. Terminal 1 is the most recently-built and caters mainly to European low cost carriers. Terminal 2 is mainly for domestic flights, and Terminal 2B is for general international flights.
The best way to get to and from the airport is on bus lines 200 and 93, which drop you off at the metro station or the train station, respectively. The airport has all the usual services like ATM's, car rental offices, banks and currency exchange office.