The centre of Cuzco is small enough to walk around, although you will probably need to catch a bus or taxi to the bus station, Sacsayhuamán or airport. Beware about walking around at night alone and/or drunk, robberies have often been reported.
Taxis are very common in Cuzco. Officially they cost 2-4 soles depending on distance. Often many drivers are not locals. Beware when using taxis at night; robberies have been reported in collusion with taxi cab drivers, at certain times radio taxis may be the safest option. The driver might also try to extort a hefty sum of money (15 soles) for a short ride if you don't haggle before - which is likely if you're just arriving at night at the bus terminal and want to avoid the hoards of touts. Just pay 5 soles and leave it at that.
If you are staying in Cuzco for a long time, the Kombis are a cheap and reliable form of transportation. These are the Volkswagen vans and small buses with names like Imperial, Batman, or Zorro. It costs about 60 centimos to ride them. If you are unsure if a certain combi will take you where you want to go, just ask. They will call out the stops as they go and if you want to get off, you just yell "Baja!", as in, "I want to get off!" They run until 10 pm. But if you are a fan of lots of personal space, this may not be the best option for you, as they tend to be quite full. Carry your backpack in front of you.
For large groups, a tourist bus can be very convenient to get to places like Pisac and Ollantaytambo. Check with one of the many local travel agencies.