Both major airlines - such as Austrian Airlines, British Airways or Lufthansa - as well as smaller companies land and take off at Innsbruck Airport on a daily or weekly basis.
An overview of the current flight schedules can be found here.
From the airport it's best to continue by train towards Ötztal. Once arrived at the station close to the entrance to Ötztal, there are public buses and taxis that take you to Obergurgl-Hochgurgl comfortably. On advance booking taxi transfer services take guests directly from the airport to the hotel and back again.
All details about your arrival journey can be found here: