The quickest and most comfortable way to reach Koh Mak is to fly into Trat airport and transfer to Laem Ngop pier in time for one of speedboats that departures according to the following time schedule: 10:30, 11.30, 13.00, 14.00, 14.30, 15.00, 16:00 and will take you to the island in approx. 45 minutes.
There are also several direct buses to the pier daily from Bangkok’s Ekkamai Bus station or Suvarnabhumi airport (5-6 hour trip), and several more to Trat City. You can also get a private minivan, taxi, or rented car for a slightly quicker journey.
Probably the most convenient option is booking a package trip from Bangkok to Koh Mak (bus + catamaran) with company Boonsiri High Speed Ferries (can be booked online).