Delta flies into West Yellowstone in the summer only. Several airlines fly into Bozeman, Billings, Cody, Jackson.
If you are thinking of staying in Jackson, try for a condo rather than hotel -- I was just in Jackson for a week and rented a one bedroom condo for about $120 a night -- another individual from work just found a rental 2 weeks before visiting -- Teton Pines or Aspens -- we love Jackson, Yellowstone and the Tetons.