In the YTL 30-40 range (about USD 18-24) at the most. The taxi companies are transparent to the customer -- just walk out of the airport and you will see a taxi line, where they are all the same. (I am sure that you could also book private transportation with a company in advance, and will be approached by the overbearing agents once you get out of customs, but I don't see any need for this and have never tried.) Similarly, catching one near the Blue Mosque will be easy.

I have always found the drivers, especially at the airport, to be courteous and honest. Most likely, they will not speak any English, but will offer you a cigarette.