OK, here's a step by step walkthrough of the first island.
Arrive. Build hammer.
Work your way through the building process to hut.
Open the locked chest and RIGHT CLICK with the shovel to dig where the X is amrked on the map.
Talk to Cap'n (Whatever his name is) and catch him a parrot. (hard and boring to do. Try going to the hill with a bunch of rocks on it, they often get stuck there.)
Dig all his gold up using the treasure map (warning: Claw monkeys spawn for one of them. Have a good weapon with you.)
Now grab all your equipment (lots of ranged weapons!!!!!!!!!) and follow him off.