The traffic in Istanbul can be miserable depending on the time and the weather you choose to travel. It is usually a good idea to take the transportation options over the sea instead of ground transportation. Unless there is lodos, the southwest wind, the seabuses, ferries, motorboats et al. are always on time. They will continue their services as long as the weather is good. Keep in mind that sometimes the motorboats continue running even the weather conditions are bad.
I'm a frequent flier and it is best for me to take the seabus to get to the Asian side where I reside.
Here is a simple guide for you to learn the basics for getting there like a local:
1. At Ataturk Airport
Once you step out of the airport (International Terminal), just look to your left and locate the HAVATAŞ (the shuttle company) stop, usually with a line in front of it.
Make sure you tell the bus attendent (who will help you with loading/unloading your luggage) that you will be getting off at Bakirkoy Sea Bus stop (Bakirkoy Deniz Otobusu).
The ride will take 10-15 min at max. It's the first stop.
It costs 11TRY (March 2014) and they also accept international currency as far as I know.
2. Check the timetable of the Seabus:
On IDO website, you can learn the Bakirkoy > Kadikoy seabus schedule.
Check out this link: https://book.ido.com.tr/Common/ScheduledVoyageList.jsp
If the link doesn't, then go to http://www.ido.com.tr/en
3. Take a Cab from Kadikoy near Seabus Station:
Once you get off at IDO (Seabus) station, you can easily locate the cabs waiting in line for customers.
That's another problem though. Some cab drivers like to "detour" before they take you to your destination.
You can learn about the fair beforehand by checking websites like http://taksiyle.com/en and make a deal with the cab driver before you get in the car.
Negotiating is a part of Turkish culture, so this will not be mean or anything.
It could work like this:
> You tell the driver where you want to go by showing the address.
> Let's say you checked from taksiyle.com and learned that the fare will be ~20TL. So, you can offer the cab driver 25TL for taking you to your destination.
> This way, you could be somewhat sure that the fare will not be more than 25TL.