From Bangkok to you can take an overnight train from Bangkok all the way to Chumphon. You can check train timetables here at Seat 61 or with a travel agent. The trains are inexpensive and comfortable with a reasonable bed so long as you book in advance. Once you arrive in Chumphon it is easy to arrange a ferry ticket to Koh Tao from the station. There is a Lomprayah (ferry & bus company) office there and you can book your transfer to the pier and ferry ticket direct. A travel agent can arrange a joint train and ferry ticket from anywhere in Thailand.
Travel agents in Bangkok can arrange a combined ticket for a bus to Chumphon pier and ferry to Koh Tao, this is normally a little cheaper than a train ticket. There is a choice of ferry companies that operate daily services to Koh Tao from Chumphon: The Lomprayah Catamaran or Marine Passion operate during the day or you can catch the night ferry. Check with your travel agent which one they have booked for you.