Because Ko Samet is three hours away from Bangkok, it is a popular destination for people with only a limited time in Thailand. It is relatively easy to get there.
First, go to the Eastern Bus Terminal in Bangkok (Ekami). The city you want to go to is Ban Phe. However, as soon as you enter the main entrance of the bus terminal you will see a sign that reads "Ko Samet." Most of the buses are air-conditioned and the cost of a ticket is around three dollars. The buses also have bathrooms. They show dubbed American movies on the trip as well and offer a snack. There is even an attendant to take care of your needs. The bus ride is about two-and-a-half hours long and offers a good glimpse of the Thai countryside.
Once you arrive to Ban Phe, go directly across to the docks. There will usually be a boat waiting to depart. The guides say you can arrange a cheaper price with some of the locals, but is probably easier just to take one of the scheduled boats that run from 8am to 5pm. Either way, it only costs a couple of dollars. Be prepared to do some scrambling over boats to get to the boat that you want. The boat ride is about thrity minutes from dock to dock. As soon as you arrive, you may think you are in anything but paradise. Just take a songthaew or walk to the national park where a majority of the accommodations are. It is about a fifteen minute walk to the national park from the dock.
Returning to Ban Phe is the same process. However, to catch the bus back to Bangkok, don't get sucked into the minibus deals. Just go right off if you are facing away from the docks and catch the bus again. You'll find plenty of people to ask directions to the station.