Budapest Airport (Ferihegy)
http://www.bud.hu/english

Transport from Budapest Airport to Budapest (16 km to the city center)
http://www.bud.hu/english/transport

Railways of Hungary (MÁV):
http://www.mav.hu/english

Search for trains:
http://elvira.mav-start.hu/elvira.dll/xslms/index?language=2
or Germany and Europe
http://www.bahn.de/i/view/GBR/en/index.shtml