From Antalya Airport there are airport buses (Havas) that operate every hour. They cost approx. 10TL and bring you into Antalya Bus Station (Otogar).
From there local buses (dolmus) leave regularly for Kas. The journey takes 4.5 hours and costs approx. 25TL.
From Fethiye Bus Station (Otogar) you continue with local bus (Dolmus) to Kas, which takes about 2 hours and costs approx. 16TL.