Krakow is a pretty small town. We didn't realize just how small til we arrived. If you look on the map, you can see the center (Stare Miasto) is surrounded by a ring road. It's incredibly easy to walk all throughout this center, not to mention beyond. Our first evening, we were wandering around Kazimierz (the Jewish quarter), and decided to walk across the bridge to the other side of the river. It's not far at all from the center! I was surprised and I think this may have influenced my choice of accommodation. I remember thinking some hotels or apartments looked out of the city but actually the city is very small so keep this in mind when you are booking your accommodation!
Also, we never used public transport except for our trip to the Wieliczka salt mine. This bus took twenty minutes just to get from the train station to the other side of the city center!! It would have been faster to walk and get on the bus at a later stop!
If you do need to use the bus, you can buy a ticket from a machine on the bus, but you will need coins. Some bus stops (like those at the train station) take ten or twenty zlotych bills as well as change.