The airport serving St. Anton am Arlberg is located in Innsbruck. Kranebitten Airport is the largest international airport in Tyrol, where most of the visitors to the ski resorts in the Alps fly to. In winter, Kranjebitten is often congested, so buy your tickets in advance. It is considered quite challenging among pilots because of its close proximity to the mountains.
A map of Innsbruck Airport can be found here.
For more information about schedules or buses and other transportation, visit the Innsbruck Airport website, in this section.