I did something which turned out to be not so good. I copied my VM to a spare disk and then reinstalled OS X and Fusion. I was hoping that once everything was reinstalled, I could simply copy the VM back to the Virtual Machines folder and it would show up in Fusion's list of Virtual Machines. Not happening. Can I extricate myself from this unfortunate situation?
Never mind! I simply selected Open from the File menu and I'm back in business.
You can also drag the VM from the Finder into the Virtual Machine Library window, after which it will be available that way. It took me a while to figure this out too.