For an overview, you can (and should) read the Wikipedia article the subject, herehttp://en.wikipedia.org/wiki/Electrolysis_of_water I think that Wiki article is a good introduction, but maybe a little short on practical hints, like what materials to use for the electrodes and the electrolyte, and what sort of voltage, and/or current, is needed to make the reaction happen. Regarding voltage and current, the two most important principles to understand are: (1)The reaction rate is proportional to the current. That is to say electrons are one of the reactants. If you can push electrons through your cell faster, you produce gasses faster. (2)There is a minium voltage needed to make the reaction happen at all. I think it is somewhere around 2 volts. Putting more voltage across the cell will tend to increase the current, and thus make gasses faster, but at the expense of wasted power, which goes into heating the cell. I think a good compromise between gas production and wasted power is to try to run your cell at voltage between 4 and 6 volts. Moving the electrodes closer together can improve efficiency, by making the paths for ion conduction shorter, and thus lowering resistance.http://en.wikipedia.org/wiki/Electrical_resistance_and_conductance However making the electrodes too close together, may cause problems in keeping the gasses from mixing with one another. Also if the electrodes are so close they can actually touch one another, then that's a short circuit, and you probably don't want that either. If you get really serious about the power supply for your electrolytic cell, you may decide you want some sort of electronic regulation, e.g. constant current, or a firm upper limit on the cell voltage. And here's one example of somebody who has engineered a power supply intended for the electrolysis of water.http://www.powerstream.com/dc-hydrogen.htm I'm not saying their box is actually worth its circa 200 USD sticker-price. I'm just saying they've at least thought about it a little bit, and it is interesting to look at the solution they've come up with. Regarding the electrodes and electrolyte, you want to choose materials that are unlikely to participate in chemical reactions that compete with the reactions you want to happen. For example if you chose NaCl (table salt) for the electrolyte, then Cl- ions may compete with OH- ions at the anode, giving you Cl2 gas in addition to, or instead of, O2 gas at the anode. A better choice would be Na2CO3 (washing soda) or NaHCO3 (baking soda). You might be asking yourself, well why don't the CO3-2 ions try to come out of solution as CO2 gas at the anode? Or why don't the Na+ ions try to plate out as Na metal on the cathode? And the answer to that question is essentially that certain chemicals, certain ions, like to stay dissolved in water. They really like the water. So much so, that just a few electron-volts is not enough energy to compel them to get out of the pool. For ions that are really water-soluble, like Na+, often the best way to get them out of solution is to put the whole swimming pool on a hot plate, and boil the water from under them. Anyway, for the novice, it is really hard to guess at what kind of chemistry might happen for a given choice of materials, e.g. which ions are likely to stay in solution, which are likely to leave. For that reason it may be best to follow someone else's recipe, e.g. carbon electrodes, baking soda, and a 5 or 6-volt power supply.