There is pram connection between continent and island. There is Rohuküla port in continent what takes You to Sviby port in island. It goes once or twice in a day.
Look into web page for more detailed information.
The best way to see whole island is to rent bikes! Really it will be great experience for you! You can rent them at HulloTrahter. Prices are ok, but bikes are real disaster! Anyway you can check it out! :) Greatest thing you can do with bikes is just to wander around for whole day, go from one side of the island to another and chill out ;)