There are no trains on Phuket.
Car and bus
Phuket Airport is situated 32 kilometers north of Phuket Town. That seems far away, but the island's capital is not the main destination for tourists. They go to the holiday resorts on the west coast closer to the airport. The airport is easily accessible by rental car. The island's main road Thep Kasattri (road number 402) runs past the airport; the exit to the airport is clearly signposted.
Upon flight arrivals, the Airport Bus leaves for Phuket Town's center via various popular hotels.
Car rental Phuket Airport
You can find counters of car rental companies in the Arrivals Hall. Six rental companies are present at Phuket Airport: Avis, Budget, Europcar, Hertz and Sixt, and the local provider Thai Rent-a-Car. You can also book a rental car in advance using the service provided by EasyTerra; they compare the rates of several providers in a single quote.
You can find taxis outside the Arrivals Hall, but on Phuket they are not cheap. Count on a price of 500 baht for a ride to places such as Patong and Karon, and more for places further out.
There's an open-air short and long-term parking lot outside the terminal.