You initially can't do much -except gathering fruits- more items and actions will be unlocked as you progress in the game.
So just explore the islands and:
The writing "Here be Dragons" at the edge of the map means you can't walk farther at that moment:
the game map is initially just a small portion of the full map, next areas will be unlocked by defeating the enemy creatures, just report your success to the statue (Kahuna).
As soon as picking up starfish is unlocked ensure you're the leader (check the colour of the ⭐ leader on top-left, if white it's you). If one of the other members of the pack becomes the leader you will often lose the control and your instincts will guide you to join your leader. You can still use left/right to avoid troubles or pick up stuff.