The means for getting from Surat Thani to Koh Phangan is the ferry. Ferries leave at several times during the day (mainly from the Don Sak port) and take anywhere between 2 to 3.5 hours depending on which one you choose. Alternatively there is a night ferry which is a cheaper but slower option (around 7.5 hours).
The ferry will arrive at either the Haad Rin (south) or Thong Sala (west) pier on Koh Phangan. Each of these arrival points will have plenty of songathaew’s on stand by to take you to your hotel.