Step 3: Valve
Cut the inner tube on either side of the valve, then trim the rubber around the valve leaving a 12mm (1/2") skirt of rubber.
Next, find a drill bit that is around the same size as the valve you're using. For Schrader valve you'll need a 1/4" bit. Drill into the shoulder of an empty PET bottle. Remove any burrs from the drilled opening, then feed the valve into the neck of the bottle and through the new opening.
Drop a small amount of a rubberized adhesive through the neck of the bottle and onto the rubber skirt around the valve, then pull the valve so that the rubber skirt makes contact with the inside of the PET bottle. You may need to poke your fingers through the neck opening to ensure good contact is made. Allow the adhesive to dry overnight.