If you've got a fish by your door, you are on the port (left-hand, facing forward) side of the ship, and if you've got a seahorse, you are starboard (right-hand side, facing forward).
Pro tip: Know what the "fish extender" phenomenon is before you go on your cruise. At some point in Disney Cruise Line's history, guests began hanging things on these stateroom fish, and the term "fish extender" came about when the decor became more and more extravagant. The fish were initially used as places to stick mail and notes (they are still used for this as well), but now are ways to express fandoms, represent family members, and more. Frequent cruisers even join groups online and exchange gifts with fellow cruise goers by means of their fish extenders.