Havataş is a bus company which connects you from and to İstanbul’s airports. The city points are: Taksim, Kadikoy, Yenisahra and Yenikapi İDO. This service runs daily from 4 am to 1 am and each half an hour a bus departures.
The fare is 11 Liras for one way trip from Taksim to Atatürk Airport and 14 for Sabiha Gökçen Airport.
To see the routes and schedules go to: http://www.havatas.com/yolcuservisi/taksim-sabihagokcenhavalimani.aspx