Well, if I remember my high school chemistry lab experiments correctly, electrolysis of water enables the H2O molecule to be broken. So You will get two atoms of hydrogen and one of oxygen. The O2 is what you want, but the H is highly explosive. And a lot of energy is used to break the molecule apart. You are better off to get an inexpensive air pump and bubble air through the water. This creates a current, where there will be an exchange of gases at the surface of the tank. Adding O2 automatically.
There is a lot of info on u tube where people want to break up water into H and O2 for use in a car. H burns and O2 supports combustion. However, again, nobody is able to do that in a cost effective way. At least, not anybody alive. If you believe everything you read on the net.
Assuming this is for an aquarium, oxygen will only dissolve in water up to its partial pressure limit. Any more you force into the water column will immediately be expelled into the air. As long as you have reasonable water to air surface area, the gaseous exchange will take care of things itself (adequate surface area at the top of the tank, microbubble aeration, good circulation, etc). If this is for something else, I played around once with electrolysis just for fun but that was a long time ago, basically recreating the standard high school science experiment. If I recall, the two things you will need to figure out is the proper material for the electrodes so they don't get eaten away, and how to deal with the extremely explosive hydrogen byproduct. Hydrogen == Hindenburg, if you recall your history.