The easiest way to get to the island is to fly to Koh Samui (one of the neighboring islands) then take the Lomprayah high speed catamaran to Koh Tao.
For a cheaper option you can fly to Surat Thani Airport from Bangkok then take the ferry over to Koh Tao, this journey takes a few hours longer on the ferry but is much cheaper than flying to Koh Samui.
You can also take an overnight bus from Bangkok and then a short boat ride to the island. We recommend the Lomprayah high speed catamaran company.