
Let's focus on the left hand side and forget the right. If we do this, it's a simple pvc overflow. The reason that it has two sides is for stability and redundancy.
Focusing on the left hand side, the water level is governed by two parts A and P. as the water flows over the top of A it raises the level of the water in G flowing into P. The check valve is a one way air valve to allow you to suck the air out of the pipe to create a vaccuum in the pipe. This allows for the siphon to continue even after a power outage. You simply have to make sure that the water level you want and A and P coincide. You must also make sure that the pipe is air tight. using pvc glue makes this much easier. When you attach your air valve you can seal it with silicone