Adıyaman is a city in Southeastern Anatolia.
There are very few buses that go straight to Adıyaman, but if they do, they will have "Adıyaman" written on the bus itself. The two main bus companies are Adıyaman Unal and Adıyaman Gularas, which are both quite big and comfortable.
Slightly more buses will go to Malatya, where you can get a minibus to Adıyaman for about 17 TL. It's about another hour-and-a-half drive and getting the big bus straight to Adıyaman would probably be much simpler.
It's easy enough to walk around, but there are frequent buses and minibuses throughout the city.