Transport back to Phuket Town is relatively easy, local buses (rather large contraptions with wooden benches in back) run between Phuket and Karon/Kata. The fare is 40 baht per person. From Phuket Town, connections to buses to Bangkok or other destinations on the Thai mainland are available, as are shuttles, taxis and/or minibuses to transport you from the city centre to Phuket Airport.
Alternately, you can go straight to the airport by taxi, which would be more expensive (unless travelling in a sizable group) running about 600 baht. Phone number for the Phuket International Airport Taxi is +66 86 4781234.