Songthaews — shared pickup trucks with two benches in the back — are the cheapest way to get around Koh Samui, running fixed routes along the ring road between the main beaches. Flag one down, tell the driver where you're going, and pay a small flat fare when you get off; agree the price up front for anything off the main route.
Taxis are widely available but mostly unmetered, so agree a fare before you get in — drivers around Chaweng and the airport quote high to tourists as a matter of course. Rental scooters and cars are the most flexible option for exploring the interior and the quieter beaches, though the ring road has fast traffic and side roads can be steep.
To reach Koh Phangan, Koh Tao, or the mainland, ferries leave from several piers around the island — Na Thon on the west coast is the main one, with Bophut and Mae Nam also serving some routes. Boats to the outer islands and to Ang Thong Marine Park can be arranged through tour operators on any of the main beaches.