How to report and block a rogue application in Facebook

Okay, I get this question a lot, so this ought to be of some help.  Here's the situation:

You see a request from something you know is NOT a normal game application (a/k/a a SCAM!), either in the game feed:

Scam Application request from the game feed.

...or in your game requests:

Scam Application request showing up as a gift request.