? The fastest but most expensive route: Fly to Samui.
You can pickup flights from Bangkok direct down to Koh Samui for just a few thousand baht. From Samui take one of the high speed ferries across to Koh Tao island (Lomprayah Catamaran or Seatran) - these cost about 550 baht per person and take about an hour and a half.
If you shop around you may even be able to get a flight direct from your country of origin to Samui, cutting out the Bangkok bit.
? The compromise : Train to Chumphon
Thailand has a great rail service. From the airport you need to get a meter taxi to the main Hualamphong train station in town (costing about 200 baht). From there you can catch a very comfortable overnight train down to Chumphon. You can get a bed in an air conditioned cabin for under 1000 baht, waking up fresh at your destination in the morning! From Chumphon you take a high speed ferry to Koh Tao island the same mornining. This will take about an hour and a half and costing about 500 baht.
This is my preferred way to travel.
? The budget route : Bus from Bangkok
Even this isn't too bad. From the airport get a meter taxi to Khao San Road (about 200 baht). At Khao San Road you can book a combined bus and boat ticket direct to Koh Tao. This will be an overnight bus ride to Chumphon, then boat the rest of the way and should cost less than 1000 baht all in.
Look out - there are a few 'sharks' around the Khao San area, out for the na?ve tourist. My advice would be to go into one of the official looking travel agents and book with your ticket with them. Go for the Lomprayah or Seatran services, you should be able to book one of these in most agents. These are fast, comfortable services and usually show DVDs on the way down. You don't want to end up getting crammed on a mini bus or 'local' service.