How would you go about teaching (or learning) critical thinking?

In college I had a job taking notes for a service that sold notes. One semester I took notes for an intro to philosophy course taught by tenured professor who liked jerking people's chains. It was a 101/intro class that fulfilled elective requirements so it had a lot of students, not all of them interested in philosophy.

The professor singled out a group of friends who liked to chit-chat about baseball.

After the class started he started talking to that group about baseball. He make one outlandish claim after another. He pissed them off. They challenged him to defend his claims, identifying his assumption, pointing out his lack of evidence, providing baseball stats, and pointing out flaws in his reasoning.

The professor then told the class that he was supposed to teach critical thinking. He didn't think he needed to as it was inborn in most people, they just needed to care enough to use it. He said he just illustrated that idea by talking nonsense intentionally to the baseball fan students, about a subject they cared about.

Media:

There's an excellent podcast called Under The Influence by Terry O'Reilly. It's a multi-award winning, funny, very well researched look behind the scenes at advertising, marketing and in general how brands, governments, and human beings influence other human beings. Why are certain things popular while others bomb? How much of our day is influenced by a lot of money to make us feel the way we feel?

There's learning about how people think in a vacuum, when we're at our anthropomorphic best. But it's also important to understand we're very often not at our best and we're beset by a lot of forces from every facet of life -- if we understand how slight of hand and magician's props work, we'll be better placed to notice illusions and walk away from shell games.

https://terryoreilly.ca/undertheinfluence/ - master episode list at the bottom of the page

From toddler-hood we placed emphasis on pointing out advertising to our child in whatever we see. We talk about end caps at supermarkets, sale signage colours, balloons on car lots, why Costco has food samples, loss leader chickens, coupons, whatever -- many positive and fun and delicious things in life are part of marketing and advertising. They're not all bad, but it's important to notice that a certain influence exists. It's okay to feel drawn to a sugary cereal box, but it's worth taking a few seconds to recognize the efforts behind that draw. It helps to temper expectations, and to isolate the flavour/nutrition/mouth feel from the joy of getting a mystery sticker or seeing a cute bunny on the packaging.

From that point on its very easy to explain motivation, bias, dark patterns, corruption and the other less positive forces of influence that's all around us. Once they're able to read, pull up a whole bunch of different media reporting on the same (age appropriate) news event: why did this paper phrase it this way vs that paper, why was this picture chosen instead of that cartoon. Etc.

We don't think in a vacuum. Like in first year Physics, it helps to draw out all the vectors affecting a body before we begin to analyze what it's going to do.

I teach Prek. My general approach is to verbalize my thought process whenever I can - especially during reading time or story time. I read the book, but I also encourage discussions about it; what are characters doing, what is their motivation, why are these things happening? Maybe there is a situation in a book that has no possible chance of happening in reality... I can bring that up too. There is a book I like, where an alien randomly shows up near the end to Deus ex machina the problem away. We talk about this - does that make sense? Why or why not? There are a lot of wild and outlandish answers I get, and then we riff off of that.

Critical thinking is really just applying logical thinking to situations; check with yourself, does this make sense? Are there other motivations someone might have? Look deeper than on the surface, and ask questions!

I wish I had a better way, since not everyone is as naturally curious as young children are, but it's a method I've found works well enough.

In the field of history, there's a heavy emphasis placed on the different types of sources, i.e. primary sources vs secondary sources. It's not something that I've seen outside of that academic history world, but I think teaching more people about primary and secondary sources would benefit society overall (helping them to think critically about news sources) and probably relates to what you're asking.

For those unfamiliar, primary sources are sources that were actually there and experienced the thing they're describing (e.g. Ann Frank's diary when discussing the Holocaust). Secondary sources were not (e.g. a modern academic paper about the life of Ann Frank). The key thing is that one is not inherently better than the other, as both have their pros and cons. Primary sources are often more reliable and extremely valuable because they actually saw or experienced the thing they are reporting, but they may not be privy to the grander narrative or context because they are still living in the moment in question. Secondary sources may not be as reliable or factual since they obviously weren't there to experience the thing with their own senses, but they can provide a ton of needed context or explain the biases present in the primary sources they draw from.

There is a book called the unpersuadables Adventures with the enemies of science, that uses interviews with people on opposite sides of controversies to demonstrate how holding a strong opinion will change your approach to information depending on whether it supports or undermines your own viewpoint. The book was recommended here, I believe by u/gaywallet

I also recommend the book Being Wrong Adventures on the Margin of error, for a more general look at risk management, mirages, magic tricks, cons, scams and mistaken life choices. This book was fascinating to me.

The other commenters already presented some wonderful advice, I'll just pipe in with my two cents.
I think what helped me a lot was learning about all the different ways the human mind is flawed, from optical and other sensory illusions, flawed mental heuristics that may work often but not always, all the way to the various common logical fallacies that are unfortunately still very common in a lot of arguments for anything.

Essentially all this taught me that you can't simply rely on your intuition and common sense alone and unchecked, because they very easily can mislead you.

For a useful jump-off point I would recommend The Scout Mindset by Julia Galef. To shameless copy the summary of Wikipedia:

In the book, Galef argues for what she calls a scout mindset: "the motivation to see things as they are, not as you wish they were". The scout mindset emphasizes curiosity, unbiased truth-seeking, and facing reality, even if that reality is unexpected. Galef contrasts this with a "soldier mindset", which she says is a natural tendency to use motivated reasoning to defend one's existing beliefs instead of being open to changing them.

To me, the notion of "the motivation to see things as they are, not as you wish they were" kinda is at the core of the entire field of critical thinking.

For media in particular, my AP English Writing & Composition class had a huge unit on how advertisements in all their various forms appeal to the audience, how those are classified (ethos, pathos, logos), and why they may or may not work. In this and other English and history classes (some AP, some not), we had multiple essays and research projects, covering different types of sources, where we had to make an argument and support it. Learning how to do that and apply it I, and my classmates, found very helpful in learning critical thinking. It wasn't one particular instance, it was in multiple classes, multiple units, and frequently reinforced. I learned in college that not everyone has access to that style of teaching, and I wish they did.

This is going to be simple, but I coached someone today on this concept. Always be curious and ask questions. I may not know all the answers to everything but I want to know as much as I can.

Also like someone mentioned above, it's okay to be wrong. Learn from it and thrive on feedback.

I will add my two cents to the list of great suggestions others have already shared.

I teach a module on critical thinking in my philosophy of education class, and we get into a lot of interesting and rather contentious territory. There really is no consensus about what critical thinking actually is, let alone how to teach/learn it or evaluate it (even though it is on the official agenda of nearly every developed nation's education system). I bring that up because there are a number of ways it has been conceptualized and discussed that are rather fascinating and may be of interest to you venturing down this rabbit hole.

One I will briefly mention is the way Nel Noddings conceives of critical thinking's purpose having to do with appreciating the humanity of other people. She points out that it is possible (under some criteria) to have a high level of critical thinking ability in some domain yet use that to manipulate or otherwise harm people. Her idea is that whatever ideas we encounter in the world, they are ideas held by people (however vile and detestable they may be). In that context she promotes the idea that aknowledging and appreciating the humanity of others should be understood as an essential part of what it means to think critically. (Although, she wrote about this long before AI was a thing, so it would be interesting to reconsider this view in light of recent technological innovations.)

As for 'practical' advice, in my classes I frame the entire course and students' assignments around self-reflection. For example, in my philosophy of education class, students draft a rough sketch of what their positions on education are, and then over the course of the semester reflect on how those ideas fit in with other established theories, where those ideas of their own came from in the first place, how they align with historical/social trends, etc. I also try really hard to expose them to a wide variety of perspectives. And by that I don't mean just different philosophical positions, but more along the lines of trying to get them to feel for themselves that this is a huge world and people really do live differently and have vastly different feelings, experiences, values, hopes, etc.

Probably not the kind of response you were looking for, but I'll post it just as food for thought!

A lot of really good points made here already, but one that I haven't seen yet - for politics specifically, I think empathy is a really underrated part of critical thinking. It can be really easy to dismiss political positions you disagree with by focusing solely on the given words being said. But if you take the time to try and understand how a given person - presumably a decent person, as most of us are - arrives at this seemingly odd or hateful position, what their pains and fears are, then you can start to better understand where they're coming from and some of the unspoken motivations driving their position. Or, even if you don't necessarily understand right away, having empathy opens up the conversation a lot more to let them tell you exactly why they feel this way, without getting caught up in the initial outrage you might feel upon hearing they have a given position.

I think practicing how to fact check and point out inconsistencies is important. Most people encounter some form of that in school by writing essays and presenting arguments. Other activities that reinforced the concept for me include joining mock trial and playing mystery/detective video games. Now that I think about it, the games served as an exercise for a majority of concepts listed in this thread (sources, persuasion, motivation, etc.)!