The quickest and easiest way to get to Samui is to fly. The island's fabulous airport was built by "boutique" airline Bangkok Airways, which operates dozens of flights a day to Samui, mostly from Bangkok, but also from Singapore, Phuket and Chiang Mai (typically in the high season only).
There are two main ferry companies operating boats between the mainland and Samui. Most passenger ferries leave the mainland from the pier a short distance from Surat Thani town, while car ferries use the port at Don Sak. Passenger ferries arrive at the main pier in Nathon Town, while car ferries arrive at a special-built pier further south down the west coast.
Ferries to Phangan can be caught at either the pier in Nathon Town or at Bophut on the north coast. Lastly, it's worth noting that there is a combination bus / ferry service from Bangkok. Buses take you from Bangkok to Chumpon and from there a ferry travels to Tao, then Phangan and finally Samui. One tour operator to check out is Lomprayah.