Cut the PVC pipe into three 2-foot pieces and two 1-foot pieces.
Cement the PVC T center to one of the 2-foot pieces of PVC pipe. Cement the two 1-foot pieces of PVC pipe to the open ends of the T.
Cement one of the 90-degree elbows to the open end of one of the 1-foot PVC pieces cemented to the T. Turn the elbow so its open end is parallel with the center 2-foot piece. Cement one of the remaining 2-foot pieces of PVC into the open end of the elbow. Repeat with the remaining elbow and 2-foot piece of pipe onto the open end of the other 1-foot piece of pipe. You should now have a PVC "W"--or side-laying "E"--shape with equal length legs. Allow the cement to dry completely.
Drill a 1/4-inch hole into the center of two of the three PVC caps. Screw the threaded end of a stainless steel barbed nipple into each hole.
If you have the nickel plates instead of the stainless steel mesh, drill a 1/4-inch hole near one end of each plate.
Use the diagonal cutters to cut two lengths of wire 3 feet long. Use the utility knife to strip 1/2 inch of insulation from each end of both wires.
Use the soldering iron and solder to attach one end of each wire to one electrode (either one of your stainless steel mesh squares or your drilled nickel plate). Repeat this for the remaining wire and electrode. Allow to cool.
Insert one electrode (mesh or plate) into one of the outer legs of the PVC assembly. Push it down at least 18 inches. Cement one of the PVC caps with a barbed nipple onto the open end of that pipe, sealing the end and securing the electrode from slipping. Note: If the cap will not fit with the wire coming out, use the utility knife to notch the end of the pipe enough to slip the wire in but keep a tight seal. Repeat, securing the second electrode into the remaining side of PVC pipe. Allow cement to dry.
Wear rubber gloves and face shield, and mix 1 gallon of distilled water with 2 lb. of lye to make your electrolyte solution. Pour this solution into the center arm of the PVC assembly. Since the assembly legs are all the same size, the level the electrolyte solution fills the center leg will be the same as the levels in the other legs. Add more solution, if needed, to bring the level to fill the leg approximately 3/4 full. Cap, but do not cement, the center PVC leg with the remaining PVC cap.
Attach the battery charger negative (-) terminal to the stripped end of wire coming from one of the electrodes. This electrode is now the cathode. Attach the positive (+) battery charger terminal to the stripped end of the wire coming from the other electrode. That electrode is now the anode.
Attach one flexible plastic hose to each of the stainless steel barbed nipples.
Turn on the battery charger. Gas will soon form around each electrode and bubble to the top of each outer leg. The gas coming from the cathode (negative electrode) will be a mix of hydrogen and water vapor. This is usable for your experiments, but it is not safe to store. Look for other articles on how to purify, store and use hydrogen gas safely.
The gas coming from the anode (positive electrode) will be a mix of oxygen and water vapor. It is usable for experiments, but likewise is unsafe for storage until purified and properly stored.