If coming from Phuket Airport you can pick up a voucher from the airport transportation booth for a flat rate of 750 baht. The drive is just under an hour. Many hotels offer transport from airport to the hotel for 1000 baht.
You can also take metered yellow taxis - cheaper than from inside at c. 650 baht. Turn right as you exit the airport building ignore the touts and you'll see a stand at the end of the walkway. You tell your destination to the staff at the stand and they will give you a paper with the taxi driver number for you to keep in case you need to report a problem. Fares to other destinations in Phuket cost around 300 baht and up. The rate is what is displayed by the meter plus 100 baht airport fee. The meter will start with a 50 baht display. You may stumble upon a freelance taxi driver that will take you from the Airport to Patong for the flat fee of 400 baht. If the driver is pleasant, you may wish to ask for his mobile number for the return trip later. The same driver can take you from Patong to Phuket Town for 350 to 400 baht.
For those who are price conscious, the transportation booth inside the airport also sells seats on a minibus for 180 baht. The minibus makes several stops along the way to drop off other passengers.
For those who want to save even more, take a near-hourly till 20.45 airport bus to Phuket Town 85 baht as of May 2010, 1 hour. From there, go to the downtown market around 1-2 km away, but motorbike taxis will offer you rip-off prices like 40 baht, bargain or wait for a public songthaew, then wait for a bus/songthaew to Karon beach.