Hydrogen has a lot of uses in a Martian colony. Primary among these is in chemical synthesis and in smelting. On Earth, Hydrogen is largely produced from Methane or from other hydrocarbons. On Mars this is not practical because the hydrocarbons will themselves be produced from Hydrogen. While there is a small component of Methane in the Martian atmosphere (Steigerwald '09), it is at a very tiny concentration, and thus is not useful for a colony.
Hydrogen on Mars will probably be produced by electrolysis. Electrolysis involves splitting water into its components by sending an electrical current through water with some ionic compound in it. The ionic compound, known as an electrolyte, increases the tendency of water to conduct electricity. On Mars, Sodium Sulfate will probably be used because it will be available, is not corrosive, and does not react to form toxic gases. Sodium Sulfate is often used as an electrolyte in systems that are intended to electrolyze water on Earth (“Electrolysis of Water” Wikipedia; CR Scientific). Generally, the cell voltage in water electrolysis is about 6 Volts (CR Scientific). This shouldn't be a problem for a Mars colony.
It is important, when electrolyzing, to choose a proper electrode material in order to prevent corrosion and thus the need to constantly replace the electrodes. Stainless steels are good with corrosion resistance, but they contain large amounts of chromium, which will not be produced in large quantities by an early Martian colony. Graphite electrodes are highly corrosion-resistant, but there is no natural graphite on Mars and artificial graphite is generally made from heavy hydrocarbons, which will not be available on Mars. Aluminium, perhaps alloyed with Silicon or Magnesium for improved corrosion resistance, can be used for the electrodes.
Placing the electrolysis device in a centrifuge can also help to increase efficiency by making the gases float away from the electrodes more quickly (Water Electrolysis Research CVGS). Given that the gravity of Mars is lower than that of Earth, it may be necessary to use centripetal gravity to increase the effective force on the electrolysis machine to Earthlike levels.
On Earth, electrolytic processes are generally between 60% and 80% efficient (National Renewable Energy Lab '04). Given that equipment on Mars will be fairly rudimentary, an efficiency of 55% will be assumed. Water has an energy of formation of 285.8 kJ/mole. There will be one mole of Hydrogen gas produced per mole of Water electrolyzed. Including the 55% efficiency factor, this gives an energy input of 260 MJ/kg of Hydrogen gas. This is a lot, but due to Hydrogen's low molecular mass, a small mass of Hydrogen will go a long way in terms of participating in chemical reactions. Furthermore, for each kilogram of Hydrogen produced in this process, there will be 8 kilogramsof Oxygen produced from the water.
References:

"Electrolysis Experiments - Introduction." CR Scientific. Web. 17 Dec. 2010. <http://www.crscientific.com/electrolysis.html>.


"Electrolysis of Water." Wikipedia. Wikimedia. Web. 17 Dec. 2010. <http://en.wikipedia.org/wiki/Electrolysis_of_water#Electrolyte_selection>.


Steigerwald, Bill. "NASA - Martian Methane Reveals the Red Planet Is Not a Dead Planet." NASA. 15 Jan. 2009. Web. 14 Dec. 2010. <http://www.nasa.gov/mission_pages/mars/news/marsmethane.html>.

"Technology Brief: Analysis of Current-Day Commercial Electrolyzers." National Renewable Energy Laboratory, Sept. 2004. Web. 14 Dec. 2010.

"Water Electrolysis Research." CVGS Home. Web. 17 Dec. 2010. <http://www.cvgs.k12.va.us/RESEARCH/Final/sresch04/lewis/intro.htm>.