I purchased & downloaded Mountain Lion, and then...nothing happened I purchased Mountain Lion through the App Store on my 10.7.5 MacBook Pro.

The download completed and I clicked through the prompts to choose an install location and agree to the terms.

I'm sorry to say I'm not sure what happened next as I shifted my attention to another computer.

I assumed the install process was running.

However, when I looked back at my MBP, I was back on the desktop with no sign of activity.

(It's conceivable that I clicked "cancel" by mistake -- I'm kind of tired/distracted/trying to juggle several things at once today.)

I went back to the App Store, looked under "purchases," and found Mountain Lion labelled as "downloaded" (as I would expect).

How can I restart the installation?

Can I go to the downloaded file and click on it? Where would I find it?
Check your /Applications folder. After downloading Mountain Lion, the installer is placed there (entitled Install OS X Mountain Lion).

It will be deleted after installation, but should still be present on your machine if you have not upgraded yet.