The only option to get to Ko Tao is by boat. The nearest airport is in Ko Samui or Surat Thani, which is fairly well connected to major cities in the region Bangkok, Penang, Singapore, etc.
From Surat Thani (From The South)
If you're coming from the south, you can take a ferry from Surat Thani around 3 hours for the morning ferry on the mainland, or from Ko Samui 1.5 hours or Ko Pha Ngan 1 hour. If you're taking a boat from Surat Thani by Bus or Train, one possibility might be an overnight ferry - depart around 23:00 and arrive in the morning, about 06:00 subject to changes. It's advisable to arrive early to grab a mattress as most are formerly cargo boats, so facilities are basic.
From The Other Islands
You can also day trip on diving charters from Ko Samui. Many have high speed boats that can make the trip to Ko Tao in about an hour.
Lomprayah High Speed Catamaran or Seatran are the fastest and most comfortable way to get to Ko Tao. They run twice a day from Ko Samui, Ko Pha Ngan, Surat Thani, and Chumphon. They also have online booking - useful for checking availability at peak times -, and all their boats have air conditioning and movies for all passengers.
From Bangkok / Chumphon (From The North)
The northern terminal for the island ferry service is Chumphon. Numerous agents sell tickets for a variety of boats of varying size and speed. The fastest takes about 90 minutes, the slowest almost 5 hours.
These ferries only depart Chumphon at 07:00, 13:00 and 23:00/00:00. The ferries at 07:00 and 13:00 are the normal passenger ones offered by Lomprayah, Seatran and Songserm, the late night ferries are normally vehicle or cargo ferries, making for a slower 5-6 hour trip, arriving at 5AM and less comfortable ride. If you are arriving via bus or train, be sure to arrive well before the ferry times, as the ferry terminal is around an hour from the train station, and a missed connection either results in a late night trip on the vehicle/cargo ferry or an overnight stay and a 05:30 start to catch the bus to the ferry terminal for the first ferry the next day.
Sangserm offer "VIP" combined coach and boat tickets from Bangkok, claiming to take 6 hours by bus and 1.5 hours by boat - in fact, it takes closer to 9 hours by bus and 3 hours by boat, neither of which are particularly comfortable.
The best trick, if coming from Bangkok, is to book Sleeper Train #85 leaving Bangkok around 17:30 and arriving in Chumphon at 03:57 and then have a ticket booked for the 07:00 ferry. Most ferry operators can pick you up from the station where you can while away the 3 hour connection gap. You can also buy your ferry ticket at the station when you get off the train at 4am. Lomprayah have a ticket office and a ticket on a waiting comfortable large bus is included in the price.