The Budapest Ferenc Liszt International Airport (BUD, http://bud.hu/english) can be reached easily from all cities using normal or low-cost carriers.
The city center is accessible by taxi, minibus, or public transport.
Minibus (provided by airportshuttle.hu, about 11 EUR per person, one way):
Taxi (provided by Főtaxi, about 22 EUR, one way):
International trains usually arrive at Keleti railway terminal: take metro M2 to Kossuth Lajos tér to get to the city center.
The currency of Hungary is the forint (HUF), 1 EUR is about 310 HUF. You can usually pay with credit card, and often euros are also accepted.