Central Trondheim is small and flat — almost everything in the centre is within fifteen minutes on foot. Bakklandet, the cathedral, the central square, and the harbour all fit comfortably inside a one-kilometre walking radius.
Buses (run by AtB) cover the wider city; you need them mostly for Ringve, Lade, and the Trondheim Airport bus. Pay by tapping a contactless card or by the AtB app — cash is not accepted. The Gråkallen tram line is the world's most northerly tram and runs from St. Olavs gate up into the Bymarka forest; it is worth a ride for its own sake.
Bikes are easy: the city has a public bike share system in summer, plenty of dedicated lanes, and — to deal with the hills around Bakklandet — the Trampe bicycle lift. Taxis are plentiful but expensive, as anywhere in Norway. Driving in the centre is fine but parking is restricted and not cheap.