There is no actual major airport at Kitzbühel so travelers will have to fly to one of the regions other major airports. The nearest options are Salzburg, Innsbruck or Munich.  Salzburg International is actually the closest airport to the resort town and there are regularly scheduled bus and train service available. Trains average about two and a half hours, but buses generally a little less because of a more direct route.
Additionally, rail is also an option from Munich or Innsbruck, as well as other European destinations. The Eurostar line offers service from across Europe including London and Paris.

Likewise, rental cars are available at each of the major airports and driving to Kitzbühel can generally be pleasant enough. The A12 motorway will get you to the close to resort area from Innsbruck. The highways and other roads are modern and well maintained in Austria. The mountains of Austria can make for an impressive sight whether you're traveling by car, bus or train.