There are hourly flights from ThaiAirways BKK to Phuket, as well as other airways like BangkokAir. This is the fastest and most easy method, about 2500 Bath one way.
You can go by bus, this is the most cheap method.
You can go by car and drive yourself. The road is good, mostly highway, about 1000 km, that is nearly 8 hours driving. When I was going it up in November, there were some parts in repair from monsun, but no traffic jam. There are two possibilities, you can drive SuratThani and make the bend there or you can go over Ranong.