I would start by simply putting everyone through a course in deductive reasoning at the earliest age possible: https://en.wikipedia.org/wiki/Deductive_reasoning

From there you can go into the whole spectrum of critical thinking approaches, and then on to what's basically the liberal arts e.g. philosophy, social sciences etc. as you desire. But the value you get from all of those things depends heavily on the framework you have for thinking about them going in.

Claiming random things are "fake news" would be a lot harder if people could work out what is and isn't fake by themselves!