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.