The nearest airports are in Chumphon, Ko Samui and Surat Thani. Ko Tao can then be reached by numerous ferry and high-speed catamaran services.
Nok Air sells a Bangkok to Ko Tao, air-sea combi ticket online. It includes a seat on one of their twice daily 86-seater turboprop services between Bangkok (Don Muang, DMK) and Chumphon Airport (CJM IATA), followed by a transfer to the ferry pier and a Lomprayah catamaran to Ko Tao.
If you have purchased a separate flight ticket, then various ferry operators have booths in the airport arrivals area selling ferry tickets which include a bus to the pier.
The closest port to Bangkok for the island ferry service is Chumphon. Numerous agents sell tickets for a variety of boats of varying size and speed travelling in from the north. The fastest takes about 90 min, the slowest more than 5 hr.
There are two high-speed ferry operators from Chumphonː Lomprayah and Songserm. Their websites both have timetables and allow you to buy tickets online. They also both offer pickup services from the train and bus stations and from hotels.
Another option is the night boats, generally leaving at some point between ten and midnight, and offering bunks in large dormitories with fairly basic facilities. There are three operatorsː
All of these can be booked through the Salsa Hostel in Chumphon (+66 77 505005 or +66 89 4880321), who also arrange pickups.
A good solution if coming from Bangkok is to book "Sleeper Train #85"; leaving Bangkok at 19:30 and arriving in Chumphon at 04ː13 and then have a ticket booked for the 07:00 ferry. Both ferry operators can pick you up from the station where you can while away the connection gap of several hours. You can also buy your ferry ticket at the station when you get off the train. Lomprayah have a ticket office at the station and a ticket on a waiting bus is included in the price.
If you're coming from the south, you can take a ferry from Surat Thani on the mainland with a travel time of around 3 hr. Catamarans are operated by Lomprayah and Seatran Discovery. If you're taking a boat from Surat Thani, one possibility might be an overnight ferry. These depart around 23:00 and arrive the following morning at about 06:00 (subject to changes). It's advisable to arrive early to grab a mattress. As most of the boats are formerly cargo boats the passenger facilities are basic.
Bangrak Pier (aka "Big Buddha Pier) is your best bet if you are arriving at Ko Samui Airport (~10 minutes via taxi). Or are staying in Chaweng Beach area. Seatran Ferry has several trips to and from Ko Tao's main pier (Mae Head). Seatran has large modern ferries, ~2 hours and 600 baht one way as of 2017.
Maenam Pier is about 45 minutes to an hour from Ko Samui Airport. To confuse things, it is also known Lomprayah Ferry Pier (for company operating two trips to Ko Tao).
Nathon Pier is much further away from Ko Samui Airport than the above.
You might make the trip on diving charters from Ko Samui. Many have high-speed boats that can make the trip to Ko Tao in about 1 hr.
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 passengers.