Taxis and city shuttle buses can be found on the ground floor of the domestic and international arrival halls. Taxis are metered, and a taxi form the airport to the Shangri-La Hotel takes about 50 minutes and costs ~100RMB (including the express way tolls).
Tip for Airport taxis in Qingdao:
Always find properly labelled taxis at the Taxi Stand (24 hours) outside of the airport terminal. DO NOT take any "taxis" (or just cars) outside of the Taxi Stand area. Avoid especially drivers inside the terminal at the Arrivals lobby who tell you they can give you a fast and cheap ride. The fare from Qingdao Airport to Shangri-La Hotel should be around RMB 70-100 (<US 18). Time needed to get downtown is about 35-45 minutes. Safe travels and see you all soon!