The nearest airport is Budapest Ferenc Liszt International Airport (BUD). Upon arrival take a bus to Ferihegy vasútállomás (8 minutes). From here take a train to Szeged (2 hours). The festival is a 30 minute walk from the station or you can take a cab.
Szeged is accessible from most European cities but requires at least one transfer along the way.
Yes, there is a dedicated festival campground.