It is very important to note you need the oxygen as well for it to actually add mileage to your car. Also, your car must be a recent model with a smart controller, else you'll just wear out your engine faster.
There's many plans for making the fuel cells out there, but I would suggest you try to use electrodes made of hard carbon (different from normal moulding carbon, mainly used for fluorine production). If that is not obtainable (probably isn't), go with stainless or high-nickel alloy steel, there may also be special corrosion resistant steel, which is basically high-nickel steel. A good place to get materials would be
http://www.mcmaster.com, they also sell thick-walled ABS or PVC like you'd want to make your tanks out of. For your battery, I would choose lead-acid. They are easily refillable, requiring lead… and (sulfuric) acid. You can buy 80% sulfuric, which must be diluted, as drain cleaner. Look at the label. You could also probably buy it from a store specializing in lawn equipment or batteries. Once the lead plates are completely dissolved, buy a new battery.
Also, do not forget a flame arrestor. Enough brown's gas is produced to make it asplode quite awesomely. (I once made a Brown's Gas torch for soldering precious metals… part of it asploded. Not fun.)