I know how land siegs work, surround a city choke keep anything from coming in or out and if you feel up to it you can try to storm the walls by force. But how do Island sieges work, at least when it comes to assaults?
In some situations, if you planned ahead of time, just like a land siege, you can have people on your side make things go....in a favorable direction.
However, even with that in mind, you still have to deal with how to assault it; do you launch a surprise assault as sunrise, or sneak through the dead of night and try to make an opening into the island's main defenses?
EDIT: Also, as B-29 said, depending on how big of an island you're talking about, you should do different methods. Sieging Malta, you could blockade it, and not let anything get past, but the same can't be said if you're sieging a place with lots of high terrain, ie Sardinia or some of the Pacific islands.