All major airlines fly into either Suvarnabhuni or Don Mueng airports. There is a free shuttle bus between both airports.
You can read all about getting to Koh Tao via 'Koh Tao - a Complete Guide'.
You can also travel to Koh Tao via a bus and ferry from Bangkok. Lomprayah offers a bus and ferry service which takes approximatley 10 hours including the ferry to Koh Tao. For more information, refer to 'Koh Tao - A Complete Guide'.
There is an overnight train from Bangkok to Chumphon. Following which you will need to take a ferry from Chumphon to Koh Tao. For further information, refer to 'Koh Tao - A Complete Guide'