There are a lot of car rental places in Ankara, locally owned as well as chain franchaises. If you are looking for a centralized location to find many car rental companies in the same place, try Tunus Cd. which runs parallel to Ataturk Blvd between Swan Park and Kennedy Cd. in Kizilay. South-west of Kocatepe Mosque.
Here, you will find major companies such as National, Avis, and Budget. But along with these major chains, there are also smaller Turkish companies offering cheaper rates. Try them first. Also, there are plenty of local car rental places in every area of Ankara.
Renting a car is easy if you are renting a standard/manual vehicle. Depending on the model, a standard/manual car can cost anywhere between 50-90 TL per day. However, if you are North American and can't drive a standard, you will need to book a few days ahead in order to get an automatic car. Also, the automatic vehicles stocked by the larger companies tend to be very expensive models and can cost up to 300TL per day. If you book ahead with the smaller companies, you can get a basic car for 70TL a day. The automatic cars rent for more money as a general rule and there is only a couple, if that, per local company.
Also, before driving off in your rental car, make sure you know how to drive the car. Some of the automatic models you will see have both a manual AND an automatic setting, which can be difficult if do not know how to switch between the two.
Bring your driver's license and passport.