Adıyaman is a city in Southeastern Anatolia.
There are buses that go straight to Adıyaman and they will have "Adıyaman" written on the bus itself. The three main bus companies are Adıyaman Unal, Adıyaman Gularas, and Metro 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.
It's easy enough to walk around, but there are frequent buses and minibuses throughout the city.