As a non-academic, how do I find papers that reference a certain article?
Google Scholar can get you quite far.

Go to scholar.google.com and paste in the full title of the paper you're looking for.  Here's one of mine:



Click the "cited by" link (highlighted) and you'll get a list of works citing the paper you're interested in.  Some of these will be papers, some won't, and Google's indexing isn't quite the same as some of the other sources.  But it's close.  For each of the citing papers, there's an "All n versions" link.  Browsing those versions will often get you to a legitimate copy from the author's institutional repository (see the right-hand column), ArXiv, or various other sources; the Unpaywall browser extension can also help track these down.