How do I use hundreds of different photos as components which, when
combined, form to create a single image? The only immediate example
that I could find of what I am talking about is a small political
photo:
http://www.michaelmoore.com/_images/home/george-faces.jpg
I'm assuming there is a program that exists out there that does this
automatically, however, since I do not even know the name of the
process, I am unable to successfully search for it. Does anyone know
the name of this process and a program that is available for download
or purchase to perform it?

I think at least one term for the process you're talking about is "photomosaic."

Searching on that term ought bring you some more information on the
process, providers, inventors, etc..

Some of the material in this answer to a similar question may be of
interest to you:

http://www.answers.google.com/answers/threadview?id=385566

Here is a program you can try for free from download.com, a trusted
source for downloads.

http://www.download.com/Mosaic-Creator/3640-2192_4-10225432.html?tag=tab_ur

Good Luck.