Originally Posted by railways

In this instance, I would definitely recommend taking a taxi. Under no circumstances engage with the touts with official-looking badges who meet every international train – they are con-merchants. Your best bet is to stand outside Keleti station (exit to the area to the left of the main station building as you arrive) and call a cab (don’t take any arriving or lurking cabs). City Taxi is reputable and has helpful, English-speaking operators who will tell you where to wait, what type of car your taxi will be, what its number is, and how long it will take to arrive (generally less than 10 minutes). Ask for the (fixed) transfer fare to the airport – it is currently a reasonable HUF 4,800 – about €18.

As an alternative to all of this, there are bus services direct from Vienna Airport to Budapest (Nepliget, on the airport side of the city and on metro line 3) operated by Eurolines and Orangeways.