Installing Snow Leopard onto an external drive isn't very much different than installing it onto your internal drive over your current OS.
First, buy the Snow Leopard DVD. Apple and many retailers sell it for about $30.
When the DVD arrives (or you get home from the store with it), run whatever system maintenance you're comfortable with (Verify/Repair Disk and Repair Permissions using Disk Utility at the very least) and then back up your hard drive. I suggest both a full bootable backup onto an external hard drive plus a separate backup of your most important data (purchased music and movies and other media, your dissertation and other text files, etc.) on some external drive or removable media such as writeable CDs or DVDs.
When the backup is complete, connect your blank external hard drive (NOT the one you used for your bootable backup!), then insert the Snow Leopard DVD. Find the "Install Mac OS X" icon (it might have a slightly different name) and double-click it to get the installer started. When it asks you to choose the disk onto which to install Snow Leopard, select your external hard drive. The rest is fairly automatic.