To assemble the pipes system of the island, you need to connect all the pipes to pumps (the elements you can't move). You can turn the pipes as you like and buy additional parts from the Market. We've attached screenshots:)

P.S. You only have access to the pipes section of the Market while you're on the Hidden Island or in the Ancient Pyramid. You can't buy additional parts on your Home islands!

Hidden Island:

Ancient Pyramid: