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. The fare for a Lomprayah ferry is 750 baht (as of May 2022) and can be as low as 550 baht if there is a special promotion running.
Another option is the night boats, generally leaving between 10pm 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.