I was wondering how a person could break down a chemical compound. For instance, could you break water down into pure hydrogen somehow? How would you do this? If you can break down chemical compounds how would you do it?

There are various ways of decomposing chemical compounds. In the case of water, it is done by electrolysis.

Electrolysis of water - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Electrolysis_of_water)

There are some chemical compounds that can be decomposed into their elements simply by heating. The rule is that you have to provide the energy that lies within the chemical bonds. You also have to prevent any side reactions from occurring. In most cases, the latter is truly difficult.