Buses #200E (daytime) or #900 (nighttime) - take the bus to Kőbania Kispest metro station. Travel time will be about 30 minutes. Tickets cost 350 HUF if bought at the airport building and 450 HUF if bought from the driver.
Train - trains run every 25 minutes from the station from Ferihegy to Nyugati station in the city center.