Getting around Phuket is easy although may be expensive if you are in a weak bargaining position.  There are a few options available, and choosing one depends on a personal preference. 

Costing between 150 – 350 Baht/day, motor bikes are available for hire all over the island.  This is a good option when planning extensive exploring.  If choosing this option, make sure to inspect the bike for pre-existing damage before renting it, to avoid being charged later. Inspect tire condition to ensure there is ample tread as roads can be slippery and test the brakes. Take pictures of your bike.

Another thing to consider before hopping on a motor bike is that driving is done on the left hand side of the road throughout Thailand.  Also, note that motorbikes are the greatest cause of serious injury on the island. 

Do not leave your passport with a motorcycle rental company. Many will insist you must leave it to rent a bike but there are many who will rent it without enforcing this. Why would you leave your only way out of the country with a company you know nothing about. 

Riding on the back of a motorbike taxi is another option for getting around.  This is the most inexpensive of the transportation options, but is not always comfortable.  Make sure to request a helmet before ever getting on a motorbike.  Not only is this for safety, but police will charge 500 Baht for anybody breaking the helmet law. 

Other options for getting around are Tuk Tuks (three wheeled, open aired taxis), taxis, busses, and car rentals.  All of these are readily available and fairly inexpensive, with car rentals costing the most. You might want to use caution when taking Tuk Tuks around Phuket. They can overcharge and together in concert which means they have agreed a price and do not waver from it. There has been some incidents of some drivers being overaggressive to passengers.

You can rent cars all over the Island and can expect to pay 1,000 to 2,000 Baht per day depending on vehicle type and length of rental time. The expected amount for a small compact car would be 1,200/day high season and as low as 800 a day low season. High season many car rental companies have all cars rented out but in the low season many have most of the cars available and you have better bargaining position. 

If you are planning to play golf in Phuket, book the package of Green Fee, Caddy Fee & 2-way Transfers as the golf agents provide the transfers cheaper than private taxi services. 

Long tailed boats are the most common form of local water transportation. 

This is may be the best Phuket Map site right now, with some excellent static maps and video journeys.