Friedman Memorial Airport at Hailey, 12 miles south of Ketchum, takes commercial flights from Seattle, Salt Lake City, Denver, San Francisco, Los Angeles, and Chicago. The runway is short and surrounded by mountains, so cancellations and diversions to Boise or Twin Falls happen in bad weather. Build a buffer into your return plans.
The alternative is to fly to Boise (BOI) and drive — two and a half hours up Highway 20 over Galena Summit, scenic and routine in summer, occasionally hairy in winter when chains may be required. Salt Lake City is about five hours' drive if you are coming from the south.
A free local bus, Mountain Rides, connects Ketchum, Sun Valley, Hailey, and Bellevue all winter and most of summer. It is reliable and saves the parking hassle in town.