jxn-
You don't need to create a partition to use Damn Small. Just pop the cd in and you'll be fine.
Now, if you wanted to install it (or any other distro, like Fedora or Slackware) to your computer permanently (so that you didn't have to use the CD each time) that's when you'd need to partition your hard disk.
But to just use any live cd distro, you shouldn't have to do anything with your hard disk.
All live-cd's aren't all the same in term's of 'bare requirements' if you are talking about the level of hardware required (RAM, CPU speed etc.). Some are very small/lightweight and only take you to a command prompt for the purposes of rescue/repair etc. Others, like
knoppix are pretty much full fledged distros, requiring faster hardware and launch you into a feature rich GUI.
If you can convince the lady at the pc shop.. that I'd like to see.