Where do I place hook_cron()? I think I need to use hook_cron() to cause my new module to be run each time cron runs, but in what file and directory do I place this code? Is it in my new module or some other place. 

Logically, it would seem that it should go some place other than my module, but I don't know where even though I've looked at documentation from various web sources. It seems like the "chicken &amp; the egg" problem. If I put hook_cron() in my module how does Drupal know to tell cron to run my module? Maybe it's magic?

I'm using Drupal 8.
All hooks by default go in the .module file, so it should go in the .module file.

It's not clear what you mean by "run my module", as modules aren't 'run', so I can't really give any more info.