Although Twin Falls is served by an extremely modest mass transit system, having your own car is effectively a requirement to see anything more than walking distance from your hotel. Cars can be rented at Magic Valley Regional Airport from many companies including Alamo, Avis, Budget, Hertz and National.
Rudimentary taxi service is available in the city if needed, but it's no Manhattan. Don't expect to hail a cab even on busy streets. You'll most likely have to call a service to get a ride, even if at the airport. Check the Yellow Pages.