Easiest way to get to Islands in Thailand from Bangkok?

And best to organise beforehand or organise from Bangkok.

have many ways to go to the island but you should select where will you want to go first. Coz some places easy to go.
1.Phuket, Krabi you can go by plane and have a low cost airline to service also such as Airasia, Nokair.
2.Samet in Rayong, Pattaya you can catch taxi to the port for one trip is cost 2500-3000 baths you can bargain too.
3.Other province or island good for go by bus or plane after that take another transportation another time.
***do you interested in waterfall ? if you want to go the good place is in Kanchanaburi. You can take a train from Hua Lam Phong ( head train office) and buy a ticket to Tai Yok waterfall in the morning and can back in afternoon or stay there one night. This train way you will see an amazing view coz the way built when world war II by Japanese. It's call Death station and Death hill. You can see a musium also.

Hope you have a good trip. :)

It all depends on which island or islands your talking about. Some can be reach by plane, bus or taxi. Best to have some plan before you arrive. The easiest way to Koh Samui is to fly Bangkok Airways or Thai Airlines. You can check out their web sites and see if it's affordable for you. Other ways to go is by bus from the southern bus station, it will take about 10 hours trip to the ferry and then a ferry trip for 1 and half hour. I am not sure of the price for the bus. I drive to the ferry myself and take my car over when i go.

koh samui: plane (then take boats to koh tao, koh panghan, etc from koh samui)
phuket: plane (boat to koh phi phi, koh lantha, etc from phuket)

fly to krabi on the mainland go to other islands from there.

Swim or take a boat.