Koh Samui has an international airport. You can fly to Koh Samui directly from Bangkok with Bangkok Airways, who has more than 15 flights day. Thai Airways also flies direct from Bangkok twice daily. The flight time from Bangkok is one hour, smaller planes take 90 minutes.
Another way to get to the island is by ferry from Suratthani. There are ferries that leave from Don Sak pier every hour and arrive in Koh Samui at Lipa Noi pier, on the west side of the island.