Once you have picked up all the pieces, the next step is to assemble the pieces. On the beach you will notice a spot in the middle of the screen. This is where the pieces are assembled. You have a fairly simple jig-saw puzzle. All the pieces are in their final orientation so no rotation of the pieces are necessary. Picking up and placing the pieces is fairly easy, though the program can occasionally be fussy about the exact placement of the pieces.
The whole purpose of a puzzle is to figure out how to assemble the puzzle yourself. That being said, for the sake of completeness here is the official solution to the puzzle.
As I know the official solution to the puzzle I never bothered trying other solutions. The game determines if the puzzle is compete not by looking at piece location but by checking to see if the surface area is entirely covered so it may be possible to solve the puzzle other ways than the above solution. If you have an alternative solution, I would love to hear about it.