1. Right click on the NetworkManager status icon to open the settings menu and choose "Edit Connections"
  2. Click on "Add" on the Wired tab. Yes, you can have multiple connection profiles set up even if you only have one Ethernet port.
  3. Choose the "IPv4 Settings" tab for the new connection and change the Method selection to "Shared to other computers".
  4. Name the connection in a way that makes sense to you (I chose to call it "Shared Ethernet"), click Apply.
  5. Connect the other computer or switch with an Ethernet cable, and choose the just-created connection profile as the active one from the NetworkManager connection menu. You're done.

When you're using the Ethernet port for a regular LAN link, just choose the original network profile instead (mine's called "System eth0"). That profile probably is the one that is used automatically, so if you make this new one not automatic, you'll just have to choose it when you want to share an Internet link and plug in to something.

Now, if I could just figure out how to do the same with Mac OS X and/or Windows as well, it'd be simpler to chain to a colleague's machine and share a single wireless link instead of paying 20€ a day per computer for a conference room wireless.. Unfortunately, they make this same operation even more difficult to find and make work.