Upplands Lokaltrafik runs public transport within the city and county.
All local buses depart from the bus terminal at Uppsala Central Station, with most stopping at Stora Torget. You can buy tickets at the UL office inside the station, by downloading the UL app to your smartphone, or from numerous ICA supermarkets and Pressbyrån stores (look for the yellow-and-black UL sign).
A single bus ticket costs 37kr and can be purchased on-board most UL buses and trains by using a Visa or MasterCard credit/debit card. That said, a variety of more economical options are available, depending on how much bus travel you are planning on doing. Check out the excellent English-language homepage for details on how to save yourself money if you plan on sticking around.