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 30 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 086-478-1234.