Phuket is well-served for transport options. Its airport receives international as well as domestic flights. The bus terminal is 14 hours from the capital and links the island to destinations around Thailand, but perhaps a more exotic means of getting there and away is to island-hop it on a ferry.
Renting cars and motorbikes is easy enough in Phuket, though it's worth taking out insurance - and a helmet if you're taking out a bike. Otherwise, the public transport options around the island - everything from buses to túk-túks are plentiful and cheap.