As you arrive to the airport probably you want to go to Budapest University of Technology and Economics (BUTE).

Getting into town:
We suggest you to prefer using the Airport Minibus Service operated by the Air Traffic and Airport Administration (LRI), which takes passengers from the airport to any address in Budapest for 2880 HUF/person/route (about 10 €). It is more reasonable price than calling a taxi. You can reserve a minibus at the airport information desk or at the following number: 06-1/296-8555.
More information at http://www.airportshuttle.hu/en/

The local bus service offers the 93 bus, an express bus which runs between the underground terminus at Kőbánya-Kispest and Ferihegy 1 and 2. You need a 350-forint ticket to travel on the bus, which can be bought at vending machines by the bus stops. From the Kőbánya-Kispest station you need another ticket to take you into town. The best place to get off is probably Deák tér, where all three underground lines meet, and which serves as a terminus for a number of trams and buses.