If you want to travel from the Malaysia / Thailand border town of Padang Besar to Phuket, you will first have to get to Hat Yai, as there are no direct transport services from this small border town.
The distance from Padang Besar to Phuket (via Hat Yai) is around 500 km.
From Padang Bessar to Hat Yai there are a number of transport options available:
You can take a train to Hat Yai Junction Railway Station.
A minivan or local bus from the Thai side of the border.
Or take a taxi (available from the Malaysian side of the border - not easy to find on the Thai side).
Regular bus services depart from Hat Yai bus station (located to the south of the city) to Phuket.
The easiest / quickest way to get to the bus station from Padang Besar is to take a minivan (departing from the centre of town).
Once you arrive at Hat Yai bus station, you can buy bus tickets or minivan tickets from inside the bus station, or from agents located outside the bus terminal (these are usually more expensive - so best to stay inside the bus station).
The journey by bus or minivan should take around 5 to 6 hours to cover the 450 km distance from Hat Yai to Phuket.
As there is no railway station in Phuket, you have a choice of taking a train to Hat Yai, or Surat Thani.
1) - The best option - Take a shuttle train from Padang Besar to Hat Yai Junction Railway Station - then take a minivan from the station to Phuket (tickets are sold by travel agents just outside the exit to the station).
If you want to take a normal bus or coach, you will have to travel from the train station to Hat Yai bus station by either motorbike taxi or a songthaew.
2) Take the Padang Besar to Bangkok night sleeper train to Surat Thani, then take a bus or minivan from the station over to Phuket (you will probably have to spend the night in the Surat Thani Station area waiting for the first bus to depart).
Bangkok Air operate a flight from Hat Yai Airport to Phuket Airport.
To get to Hat Yai Airport from Padang Besar, the best option is to take a taxi, as the airport is located between Pdg. Besar and Hat Yai, around 15 km from the city centre.
You could take a minivan to Hat Yai bus station, then another minivan to the airport, but that is quite a long journey!