What experience do you have that differs from typical people which allows you to make these judgements?
How are you determining that this isn't just your own confirmation bias?
But if you want: I am a trained mathematician, so I am trained in identifying the root assumptions of problems.
I am aware of the typical ways to lie with statistics. There are books about that, everybody can and SHOULD read those. For example choosing certain time intervals, making charts not start from zero to inflate a trend, picking the aspect that best supports your claim (for example, either use relative growth or absolute growth when describing an issue - one more murder in a town can mean "crime incidents increased by one" or "crime incidents increased by 100%"). Playing with proportions, like drawing circles for comparisons and using diameter (instead of area) to correspond to the values you want to show. And so on - there are many possibilities, and they are all being used.
So, for example, if I see a chart depicting some trend over a period of time, my immediate instinct is to ask "what would it look like if the chart would start one year earlier?".
Also, I think fake news might have become a topic these days because people also get their information from social media. They often know about aspects that an article doesn't mention, so they are more often able to identify articles as fake news.
Overall, there is just one thing you have to do: try remain skeptic at all times. "Bend over backwards" as Feynman put it to disprove your own assumptions.
Nothing of that is specific to me, and it is not complicated. You just have to be willing to challenge your assumptions.
For starters, I would recommend reading those books on how to lie with statistics, and your essential Feynman. And get your news from multiple sources and compare them.
Everybody can learn about certain signs. If the person asking already knew them all, why did they ask? Then their question was vacuous, not my reply. Just because a question has an obvious answer, the answer is vacuous? What is going on in your mind? What are you driving at?
Have you ever read one of those books about how to lie with statistics? You really, really should.
Thanks for the recommendation on reading a book about stats - which would you recommend? I already work on statistical models in my job and would probably get in trouble if they didn't lead to tangible results so I might even have the book on hand.
I read a book in German (specifically on how to lie with statistics), don't know which ones to recommend in English. There is the obvious one with the name "how to lie with statistics", but it is very old. Otoh, available for free (but I haven't read it).
Feynman, too, don't forget about Feynman. http://www.ar-tiste.com/feynman-on-honesty.html
Thinking, Fast and Slow was a lot about bias, but not sure if it really gets the point across effectively.
Seeing how you interpret my comments, maybe starting with statistics is actually backwards. Perhaps start with language and communication first? Sorry if my comment sounds mean, but it really seems a bit crazy how you try to bend my comments into something outrageous.