How does Microsoft compress their operating system to fit onto a DVD? What compression do they use, and is it available to the public?

CAB and WIM files on Windows install media use LZX compression

http://en.wikipedia.org/wiki/LZX

Thank you very much for your help... Hopefully I can manage to get my files compressed as much as microsoft compresses theirs. Thanks again.

It's worth noting that you can enable some compression and some single instance when putting Microsoft OSes into an ISO by using the oscdimg tool that ships with the WAIK. For example, "oscdimg -u2 -m -o -h -b<path to etfsboot.com> -l<ISO label> <path to folder containing OS files to put on disc> <path to and name of .iso file>.iso" creates a UDF formatted ISO for Vista or Win7 installation media that is fairly compressed and single-instanced to reduce size.