my mac is running OSX 10.5.8. How do I upgrade to 10.6?

Check that your current Mac meets the System Requirements for Snow Leopard...

Snow Leopard Specs:

http://support.apple.com/kb/SP575

If it does... then you need to Purchase the Snow Leopard Disc and Install it.

Mac OS X 10.6 Snow Leopard

Would Also Recommend that you do a Bootable Clone Backup of your current Hard Drive Before attempting any Major Upgrade...

By far the easiest way to make a Backup, is to use something like

SuperDuper http://www.shirt-pocket.com/

or CCC http://www.bombich.com/