When you select an island which has a shipyard, the "Build flotilla" button is displayed. Click it to build a "flotilla". Once the flotilla is ready, you can transfer people from this island to another island (to colonize an empty one or to capture an enemy one). After that the flotilla is exhausted and you'll need to build a new one. There is a tiny ship shown next to an island which has a flotilla ready.
It's just a jam game, a week is barely enough to make it work, let alone to implement a tutorial :)