Although Ankara is Turkey's capitol city its airport, Esenboga, is very small and does not serve very many international flights.  The largest international carrier serving the airport is Lufthansa, as there is a very large Turkish population in Germany.  If you would like to visit Ankara and do not wish to fly Lufthansa, or if doing so would not be convenient for for, you can easily fly to Istanbul's Ataturk International Airport from almost anywhere in North America, Europe, or Asia.  From Istanbul it is easy to get a domestic flight to Ankara on Turk Hava Yollari, Turkey's flag carrier. Turk Hava Yollari also offers flights to Ankara from Izmir and Antalya. 

Esenboga Airport is located some distance outside of the city.  From the airport you can either take a taxi, which may be a bit on the expensive side because of the distance, or take a bus which is much cheaper. 

From Istanbul it is also possible to take a bus to Ankara.  Ankara has a large bus terminal that serves routes from all across the country.  The buses are inexpensive and reliable, but sometimes slow.