Zanzibar Island Transportation

There are shuttle services from stone town to the north for around $10 return. The most fun way to get around is by motorbike, 250cc. They are cheaper in stone town by $5. in nungwi they are $20 if you have an international permit, if not an extra $10 for a permit whether youve ever ridden a bike before or not! they are great fun, we took ours all over the whole island and found the best beach ive ever seen - Kiwengwia in the east!

These are the local transport used by the locals. They are packed with people and others hang off the back.
Very cheap.
There is a 'bus station' of sorts on a dirt parking area on the edge of Stone Town where you can pick one up to the other parts of the island. Someone will advise, various people speak a bit of English.
The 'a/c' is open sides and you will be rammed in. They are often stopped at security checks by the military/police, particularly if they see tourists on board. Generally the police are relatively friendly if rather serious! You may have to produce your documents. I have personally not heard of any difficulties with 'tips' or 'baksheesh' being required on Zanzibar.
You could try hiring your own dala-dala I suppose!

the most probable way to get to Zanzibar is the plane. The airport is very small and rudimentary, but it receives an increasing number of charter flights from Europe. It is also possible to come by express ferry from Dar es Salaam.

The locals use these small boats for fishing. They may be not very fast and comfortable, but they look nice.

Ferry to Stone Town from Dar. Foot passengers taken or vehicles.
Or fly - lots of airlines fly from other continents now direct into Zanzibar, or from Mombasa, Nairobi or Dar.
On the island, taxis or communal buses - open sided trucks (called dala-dalas) with far too many people crammed in - you have to be friendly but the open sided nature means it's not too smelly! They are dirt cheap. Taxis are fairly reasonable. You can also hire a truck to yourself for a mid-price and that might turn out to be the best bet. Seats are hard and the air-conditioning is the wind, but fine as journeys are not long.
Dhows (wooden sailing boats) or motorised fishing boats can be hired at any village for a few dollars.
Mountain biking would be ideal as the roads are not busy and it is a flat island.