<math>2H_2 0 \to 2H_2 + O_2</math>
Hydrogen is created at the cathode, and oxygen at the anode.
The reaction usually takes place at room conditions, but there is also high-temperature electrolysis (100 to 850 °C) which has a higher efficiency.
Electrolysis of water requires a relatively low voltage if a sufficiently strong electrolyte is used. The electrode potential of the H2+O2 reaction that takes place in fuel cells is 1.23V (assuming platinum electrodes). So, to electrolyze water, one must supply at least this much potential to prevent the liberated atoms from recombining, plus an additional 0.47V to overcome the binding energy of the water molecules. This is 1.70V. Electrical resistance makes it worthwhile to increase this voltage to between 2V and 6V, but simply increasing the applied voltage beyond this point doesn't produce better performance unless the total power (wattage) is increased as well. It is ultimately amperage which determines the performance of an electrolysis cell.
A parallel array of electrolysis cells operating at 100 A/m2 can release 0.000026 mol/s-m2 (0.0083 g/s-m2) of oxygen. Its output increases roughly linearly with amperage (and thus with wattage, P=VI).
At this rate, the 1.1 kg/day required by a human being requires a 1 m2 electrolysis array to operate with at least 100A (>170 W) for at least 36 hours. This rate can be increased by increasing the amperage and surface area. However, it still requires the same amount of energy: 22 MJ. Assuming 30% power loss due to resistance raises the required voltage to just over 2.2V and raises the daily energy requirement to 28 MJ. In a pure electrolysis system with 70% efficiency, this is the minimum energy that the power plant must produce per person every day for the crew to breathe oxygen produced on demand from water.