There are several companies working on bringing pocket-sized fuel cells to the market. Not all of them use the same approach. Lilliputian Systems has a fuel cell that uses butane as fuel. Butane is a hydrocarbon, which means that it's made up of hydrogen and carbon atoms. The chemical notation for butane is C4H10 -- there are four carbon atoms and 10 hydrogen atoms in a molecule of butane.
Inside the fuel cell, pressurized butane molecules split apart into ions and electrons once they come into contact with the catalyst. The ions move across the membrane into an oxygen chamber. There, the ions combine with the oxygen atoms to form water and carbon dioxide. The electrons that split from the ions travel through the electronic pathway to rejoin the ions on the far side of the fuel cell.
Carbon dioxide is a greenhouse gas. Since it's a byproduct of a hydrocarbon-based fuel cell, many consider these fuel cells to be less environmentally friendly than a purely hydrogen-based fuel cell. But how could we get around the problem of generating pure hydrogen?
One potential solution may be to get hydrogen from water. We can harness hydrogen by zapping water with electricity to break the molecular bonds and split water into hydrogen and oxygen. This is a process called electrolysis. While this will give us access to hydrogen, it doesn't make sense from a power-generation perspective -- we have to use power just to get the hydrogen and so we operate at a net loss from a power perspective. But you can also get hydrogen from water through a chemical reaction.
Using a powder of alkali metals, it's possible to create a chemical reaction with water that will give off hydrogen gas as a result. Typically, introducing an alkali metal to water causes an explosive reaction in which hydrogen and a metal hydroxide are the byproducts.
A chemist named Michael Lefenfeld created a mixture of alkali powder and other additives that react with ordinary tap water to produce hydrogen without the accompanying explosion. By feeding that hydrogen into a fuel cell, you can have a purely hydrogen-based method to generate electricity.
Using this alkali powder and a fuel cell means that you could power electronic devices just by pouring a little tap water into the charger. The water will react with the alkali powder to produce hydrogen. The hydrogen moves into the fuel cell chamber and combines with oxygen to form water and generate electricity. You'll have to replace the powder cartridges in your device in order to generate more hydrogen as the alkali converts to metal hydroxide.