You need to do the following things in order to get internet in your house:
1. Go to a Turktelecom office near you with your passport and resident visa. Note: You may need to register your address and existance with your local "mayor", depending on what area of Ankara you live in. Also, you may need your landlord's help if the address is registered in their name.
2. Set up an appointment for a service man to come and install the internet. Note: You cannot avoid having a home phone line put in, because it is needed for the internet.
3. Purchase a router/wireless router. In Turkey, the most trusted and common brand to use is "AirTies". It is not the cheapest brand available however.
4. You will get a bill in the mail every month. Internet is not overly cheap in Ankara, but it is not too expensive to afford. Expect approximately 40TL per month for basic unlimited usage.