I've done some critical thinking training with my kid. It's been pretty off-the-cuff, I'm not sure I remember that many details about it. But basically it's a sort of "Ripley's Believe it Or Not" thing, from back when they'd put more fake stuff in there to throw you off.
I'll show her a news item and ask her whether she thinks it's true or not. Then we'll discuss why.
I think something like this should probably be more codified and included in school curricula. It wasn't that long ago that you pretty much knew that the New York Times was going to be reliable and the National Enquirer was not.
Now, with Google news being a prime information source (as in, not a single source, just keywords), it's especially important to be able to figure out what is and isn't true.
Although this is important just in general. I had a really eye-opening science class ("Biology of Women," maybe) in college, pointing out varieties of bias that had completely passed me by before.