Depends from where you are going. Supposing that many travelers are staying eather at Taksim or Sultanahmet(both located on the European part of the city) I would say at least 1 hour 15 minutes. Since Sabiha Gokcen International Airport is located on the Asian side, one should depart for an international flight at least 3.5 hours before.
Sure it depends on where you are heading from and which transportation vehicle you are taking. If you do not want to take a cab or the public buses, then I would recommend you to try HAVATAS. It is a private company with big buses special for airport transportation. It departs from both Taksim and Kadikoy and directly goes to Sabiha Gokcen and Ataturk Airports. For now, they are available every half an hour and the price of tickets per person is 12 TL. From Taksim to Sabiha Gokcen, it takes 60-75 minutes depending on the traffic rush.
Here is the schedule for Taksim passengers: http://www.havatas.com/ (English version of the site is under construction but you can still check timetable from Turkish version)