There is no airport in Anafi island. The nearest airport is located in Santorini island, the most popular island of Greece, which receives frequent domestic flights from Athens and Thessaloniki. Also in summer, there are charter flights to Santorini from abroad.
From Santorini and other Greek islands, there are ferries about 3-4 times a week to Anafi island. The port of Anafi is Agios Nikolaos, just a couple of km from Chora.
To get a better understanding of the island's location, view the Map of Cyclades.