So for example, if we have a folder called "my_trip_to_Paris" located in images/stories/my_trip_to_Paris, then we can create our gallery by simply entering the tag {gallery}my_trip_to_Paris{/gallery} into some Joomla! article.

Kind of ambiguous because the "tag" would not be the actual "path" to where the images are in the images > stories > myimagefolder, yet it says to put your images in images/stories/myimagefolder, then enter the tag  {gallery}myimagefolder{/gallery} to my existing joomla page.

Problem is, that doesn't work.
Error message: JFolder: :files: Path is not a folder. Path: /home/myusername/public_html/goapplego/images/znitro-carbon/
JW_SIG_PRG

That is where the folder is with just 3 images.

Okay, I just figured it out from trial and error.  You need the path of your folder; however, you do NOT need to put {gallery}images/stories/myimagefolder{/gallery}

Instructions say to simply enter the tag {gallery}my_trip_to_Paris{/gallery}.

What you need to enter is the path to your folder within the images folder of Joomla, but in the TAG, do NOT include the word "images".  So in other words, the path would be
{gallery}stories/myimagefolder{/gallery}.

Then it works perfectly inside of an existing page!