From Germany, Austria, the Netherlands and Belgium, there are good IC and EC connections, coming from Munich, Innsbruck, Brennero to Bressanone or Bolzano.
Some trains stop in Chiusa. A bus service transports you from Bressanone and Bolzano almost every hour to Val Gardena.
The nearest airports are in Bolzano, Innsbruck, Verona, Brescia, Bergamo and Treviso.
Air Alps http://www.airalps.it/
Offers short flights for independent travelers from Amsterdam, Munich and Rome to Bolzano, Brescia and Innsbruck, which make for quick transfers to South Tyrol and Val Gardena.
http://www.ryanair.com/Offers short flights for independent travelers to Treviso and Bergamo, which make for quick transfers to South Tyrol and Val Gardena.
Offers especially for dutch travellers short flights to Treviso and Verona, which make for quick transfers to South Tyrol and Val Gardena.
low cost transfer
Transfers from Milano/Bergamo and Verona/Brescia airports to Val Gardena.