There is a taxi rank opposite the terminal building, but competition for them can be keen. There are only 30 taxis on the entire island and each taxi can carry up to 4 passengers. It can be a long wait in line at Mykonos Airport and taxis are filled to destinations like the ports so expect to share with others.
Another option is to pre-book your transfer. Taxi Phone Number: (0030) 22890 23700 or (0030) 22890 22400