It took me quite a few hours of reading to figure out how to do it, so I figured that I would post a short howto in case anyone else has had problems getting AO to run on a network where the admins have blocked all of the gaming ports. (Huge thanks to Stick for pointing me in the right direction)
1. Go to your-freedom.net
2. Register (Don't worry, it's free) and download the windows installer *linux users see below
3. Install the program and click through the wizard to find a list of servers near you
4. Download Sockscap 2.40 (or the latest version)
5. Setup Sockscap with the following settings.
6. In Sockscap, click New and add Anarchy.exe and Client.exe
7. Startup freedom's app and connect to a nearby server
8. Startup Client.exe from sockscap, and have fun!
Good luck! And use at your own risk. The network admins probably won't be too happy if they figure out what you're doing, so don't blame me if you get into some trouble.
*Linux users:
It's slightly more complicated for linux users, but I didn't have too much trouble getting it all up and running on Ubuntu 6.10. The only differences for me, was that I had to use the java based installer for freedom, and I used cedega to install Sockscap. You'll also get an error when AO starts up (something about not getting updated dimensions / using chached ones), but everything should still start up like normal. You'll need cedega to be the default program set to open .exe files, because you will start up sockscap in cedega, then start AO by starting the client.exe file in Sockscap)