On arrival in Ataturk International, you have a choice of 3 local phone service providers. As you exit the arrival gate, to the far left is Avea, in front of you is Turkcell and to the right is Vodaphone (see photos below).

Process

  • You register the phone with your passport info on the spot.
  • You will be given a SIM card with a pin. They will put it in your phone if you need assistance with this. 
  • For the next two hours you will have no service (the disconcerting iPhone is"No SIM").
  • Eventually the service kicks in but but may require you to restart your phone.

Note: Each time you turn on your phone you have to unlock the SIM with the pin they give you on registration. Don't lose the PIN!

Plans
(Other travellers please feel free to fill in the blanks) 

Turkcell:  
Unknown - At the time this was researched, Turkcell was unable to offer data plans from the airport because their internet was down!

Avea: In June 2016.. L130 6gb data and 100 mins local calls, additional L50 and u d Get 30 mins of international calling

Vodaphone
As at April 2012 Vodaphone offered 4Gb of data for a month or unlimited data for a week for for L110 (there were other cheaper plans for less data). After some negotiation they agreed to unlimited for 2 weeks for the same price. It costs an extra L10 to get the card cut for an iPad. 

You may also pay in other currencies but at agregious exchange rates (they were using L1.50 per USD when the board rate was L1.80 ie the data plan costs L110 or USD73) so best pay in Lira.

The two weeks of data is provided in two one-week back-to-back plans. This means that near the end of the first week you will receive a message saying the service is about to end. It is safe to ignore this if you have purchased a second week of data.

Coverage
Vodaphone coverage was excellent in Istanbul but in Antalya it was patchy and GPS in Antalya was worse that useless as it showed the location as bouncing around from land to sea with up to 10km hops at a time. Some commenters on the net have reported that Avea may be your best bet for GPS outside Istanbul.

Other
Vodaphone sends numerous SMSs all of which are in Turkish. Install  iTranslate for free if you want to know what they are nattering on about (it's mostly worth ignoring).