Are you saying the USB drive doesn't show up when you plug it in? But it does autodetect on another fedora install at work?
Sounds like the problem could be hotplug, or it could be that you don't have hald or udev running (these two things are integral to automounting new media).
First things first. Are you using Gnome? If you're using Fedora I hope so. Under your preferences there should be an option called "Removable Storage". Check that out and make sure you're automatically mounting new removable media.
If that's all good, then try the following: as root user, type "/etc/init.d/hald restart" and "/etc/init.d/udev restart". The name of the programs might be a little different (I'm on something debian-based so things might not line up 100%) but if you can figure out how to restart these two services then do so and see if that fixes the problem.
If that doesn't fix the problem, then type the following command as root: "tail -f /var/log/syslog" and watch what happens when you plug in your USB drive. Any error messages?