Drive a little slower than you would ordinarily, do the things you would back home and you'll be fine. Common sense is called for when driving in Thailand and Phuket. Keep an eye out for motorcycles, don't do anything suddenly.

Rent your car from a REPUTABLE international company and you'll have NO PROBLEMS with insurance, or police, or if you have an accident.

Now . . . All that said, get out and see the island. Get off the island too.  Drive up to Khao Lak (only an hour), over to Krabi (only about two and a half hours) and see just how beautiful the area really is.

 Here are some good ideas for driving in the area:

Check out:  Phuket's Best Island Drives - areas of the island that even the local expats haven't seen, with stunning sea and bay views.

The Hot Springs Drive (just 4km off the island) with spectacular unknown and deserted long stretches of beach:  Hot Springs Loop.

A car will free you up greatly and you won't have to negotiate with a taxi or limo every time you see something interesting just down the road.