There are no flights within the archipelago. Converted pick-ups or dalla-dallas (minibuses) link all major towns on Zanzibar Island, and it's easy to arrange car, moped or motorcycle rental. In general, prices are reasonable and there are few hassles, although breakdowns are fairly common, as are accidents. Considering how small the island is, it's often more straightforward, and not that much more expensive, just to work out a good deal with a taxi driver. You can hire a bicycle, if you're feeling energetic, or organise excursions around the island through a tour operator.
Pemba is a small island and getting around isn't too difficult if you have time up your sleeve and the virtue of patience. Bus drivers are usually willing to take you to destinations off the main routes for an additional fee. Otherwise, cars and motorbikes can be hired as on Zanzibar, and the entire island is great for cycling. There is no public transport on the smaller islands in the archipelago, although you may be able to find someone to rent a bike from.