When you are on your adventures around the land, keep your eye peeled for treasure chests laying around.
Oh look, there's one. Get it quick!
Stand next to it and open the menu up and you'll see an option that says "Examine", just select that.
Now I'm 10 whole Gil richer and the chest fades away. I have picked up amounts like 300 Gil in a chest so it is worth looking inside when you see one.