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.
low cost transfer
Transfers from Milano/Bergamo and Verona/Brescia airports to Val Gardena.