Electrolysis is the process by which water can be split into Hydrogen Gas and Oxygen. This is done by running a current of electricity through the water which is diluted with sulphuric acid (or lemon water or salt) because it is a good conductor of electricity. Hydrogen is a Cation and Oxygen is an Anion then near the positive ends of the current you will find Hydrogen bubbles and the negative side you will find Oxygen bubbles.
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In electrolysis, oxygen and hydrogen gas are produced at different electrodes (oxygen at the anode and hydrogen at the cathode). Since these electrodes do not have to be in close proximity, the hydrogen and oxygen will bubble upwards into separate collection vessels. If you needed to separate hydrogen and oxygen once mixed, the easiest way I can think of would be to cool the mixture to ~60K. At this point the oxygen would condense and leave hydrogen gas.
2 Hydrogen atoms and an Oxygen atom bond covalently to form a water molecule.
It means that different compounds composed of the same elements have their own unique proportion of those elements. For example, both water (H2O) and hydrogen peroxide (H2O2) are composed of hydrogen and oxygen. However, the proportion of hydrogen to oxygen in water is 2 to 1, and the proportion of hydrogen to oxygen in hydrogen peroxide is 1 to 1.
Water does not need to react with oxygen to make water!
Water