chamber sealing valve concept
You may need to go through the phases several times to understand what is happening. If you still don't get it then look over some other explanations and valves that people have built.
Phase 0: Basically just the gun in its initial state. No pressure in the gun.
Phase 1: An air source is connected behind the piston. Air enters the pilot chamber and the pressure pushes the piston against the piston seat (a port protruding from the chamber in this case).
Phase 2: Air continues to flow through the input and leaks around the outside of the piston or through an equalization hole into the main chamber. Once desired pressure is reached, the input flow is cut off and the gun is ready to fire.
Phase 3: The exhaust valve is opened and the pressure begins to fall in the pilot chamber. The exhaust must exhaust faster than the equalization hole can leak air back into the pilot. Once the force pressing on the back of the piston (due to the pilot chamber pressure) falls below the force acting on the front of the piston (due to the chamber pressure), the piston begins to slide back. As soon as the piston moves away from the seat there is more surface area exposed to pressure on the front of the piston. The jump in force due to the increased surface area slams the piston back leaving an opening for air to flow into the barrel and accelerate the projectile.
The exhaust valve is closed and a new projectile loaded. The gun is then back to it's original condition, ready for the cycle to repeat.
related linksSpudfiles thread
Spudtech thread 2
general piston valve info
coaxial piston valve
barrel sealing piston valve
piston valve comparison
advanced piston valve considerations