By plane
Phuket International Airport is 35 km to the north of Patong. "Limousine" taxis from the airport to Patong are a steep 600 baht 45 minutes; meter-taxis 400+ baht from the meter-taxi stand at the airport, ignore the touts and turn right as you exit the terminal; shared minibuses limit the damage to 150 baht but 180 baht in the Patong to airport direction, presuming you book through an agency. Even cheaper however also more time consuming option is to take the comfortable a/c airport shuttle bus to Phuket Town 85 baht, 1 hour, and switch there to a local bus to Patong, see "By bus" section. Alternatively, if you know the right road, you can get off the bus after you pass the Big C shopping center on the right the airport bus goes to the left there, and the road to Kathu and then Patong is to the right from the same intersection, and try to catch a local bus to Patong there, which also passes that intersection. Local buses to Patong are clearly marked in English and in Thai.
By Limousine
Limousine usually referrs to a larger sedan, such as Toyota Camry, with leather seats, etc. They cost around 600-700 baht to go to Kata Beach. Considering the drive is about an hour long, this is one of the best options to get to Kata Beach.
By bus
Regular buses connect to Phuket Town 25 baht, 30-45 minutes every 30 minutes or so between 07:00 and 18:00. The route starts from the southern end of the beach, after which the bus crawls through town via Bangla Road, stopping to pick up passengers, before finally heading off across the hills, and going via Kathu, then passing near Big C before entering the Phuket Town.
In Phuket Town, those buses are usually waiting for passengers near the local market 1-1,5 km west from the Phuket bus station, however, some huge almost bus-sized songthaews marked "Phuket - Patong" were seen near Phuket bus station too. If you're coming by public bus from other areas in Thailand like Bangkok or Surat Thani, as well as if using the airport bus, you will end up in this bus station. Local motorbike taxi drivers can and will offer fares like 40 baht to the market or 250 baht straight to Phuket - just walk there's a city map in the terminal, bargain hard, or just wait for an arriving songthaew; even if he's not going to Patong, he will drop you to the bus station for no more than 20 baht, or probably 10 if there's more than 2-3 of you.
As at May 2011............The above is pretty accurate.To get to the market from where the large songteows go, turn right into Phangna Rd on leaving the bus station and walk to where the road ends. Turn left then right at the roundabout immediately after. Walk along this road and you will see them several hundred metres along. Choose the one to the beach you want.The ones returning from Patong will arrive here, but if enough persons want to go to the bus station in our case six persons we were charged an extra B10 each and were dropped off there.The Writer also noticed songteows coming into the bus station heading to Patong, as well as a couple parked and then leaving next to the airport bus.