Habit: Check your emotions! (Human beings are not objective. If you feel strongly about something, it doesn't mean you're wrong, but it does mean you'll probably evaluate evidence about it differently).
Sometimes (very infrequently) a scholarly journal or researcher will retract an article, meaning that the article becomes unpublished. It happens when the article is deeply misleading, the research is discovered to be fake, or it's so badly done that the journal no longer wants to be associated with it. Often the original research is widely publicized, but the retraction is not, so that non-scientists continue to believe the research claims. Retraction Watch Database is a search engine where you can search for retractions. The results will also tell you why the article was retracted. The Retraction Watch organization website also tracks different kinds of scientific misdemeanors.
Find as many of these clues as you can in your popular source. Then you can enter them into an academic database and hopefully find the scholarly article it's based on. If you don't find it in one database, try another! Sometimes you'll need to combine a couple of clues to find the original article (for example, date of publication and journal title, or journal title and topic).