The cheapest way to get here would be to book a bus/boat ticket leaving from just behind Khao San Road in Bangkok (Lomprayah High Speed Catamaran). There are other ferry packages which will vary in price but on average, it will cost approximately 1100 Baht for a combined bus and boat ticket.
If you want to book internal flights, you can fly to either Koh Samui, Surat Thani or Chumphon and get a connecting ferry to Koh Tao. Be aware of the boat schedules to the island (Lomprayah Time Table or Seatran Discovery Trip Schedule). Cheap flights to Surat Thani/Chumphon can be found at AirAsia. Koh Samui is more convenient, but a bit more expensive with Bangkok Airways. At all the airports are tourist assistance desks that can point you in the right direction to purchase a boat ticket.