Alanya is about 2 hours drive from the nearest major international airport in Antalya and the closest to the distance between the airport and the center of Alanya, just 125 km and half an hour from Gazipaşa Airport. Antalya international airport and Gazipasa Airport opened for international flights in 2011, and serves a limited, but growing number of European destinations. Most holiday makers land in Antalya and are then taken to their hotel in Alanya by bus.
If your hotel is a bit far from Alanya, you can stand outside the hotel on the road and wait for a minibus (in turkish dolmuş) to come by and pick you up. You can stop at minibus stops anywhere on the road, mostly there are bus stops, rarely at someplaces there are not bus stops, they come in each 10 and 15 minutes and are sometimes quite crowded. Expect to pay around 2 Turkish Lira per person for the ride.