After arriving in Budapest at Nyugati PU station with the Sziget Train, it's not difficult to get to the Sziget Festival.

Once outside the station, tram line 4-6 (direction: right) will take you across the Danube within three stops. At the first stop after the Danube, you should change to the suburban train in direction of Szentendre or Békásmegyer. Filtorigat is the stop closest to the Sziget Festival entrance, from there you can easily follow the other festival visitors.

Of course you can also take a taxi, but be careful with that! Never stop a taxi on the street, you might stop a 'cowboy', a taxi driver that will rip you off. It's much better to call an official taxi. This will always be cheaper than stopping a taxi on the street.