My father did an experiment with me when I was very young. He played a game (without ever alerting me to it) where he would tell me things that weren't true to see if I'd just believe them, and if I did, I'd be laughed at. He had to work harder and harder over time to make his false information seem more plausible while still maintaining something ridiculous in it somewhere, and in this way, he trained me to think systematically, checking every aspect of an idea for validity. The result was that I never believed in Santa or the tooth fairy, and I applied the same approach to religion. He wasn't so happy when he realised that I was rejecting that. Over two decades of arguments ran through before I converted him to atheism - that's how long it can take to deprogram someone who's much more rational than average but who lacked the early training that he gave to me.

I've been studying thinking ever since (and I now work on building AGI - artificial general intelligence), and what I've found is that most people follow a simple strategy of collecting beliefs from sources that they trust, and that's all they ever do. The simply never learned to think for themselves to any great depth, but always relied on others to do that for them. This is why it's so hard to deprogram people of even the most ridiculous of religions - the main thinking skills that they develop are the ones involved in defending their existing beliefs by collecting evidence that supports them while rejecting anything that undermines them, and that's just about their entire algorithm. Substantial aspects of this broken algorithm are still in play even with highly educated people at the top of academic fields, and that's been the most extraordinary discovery: it's right there in the majority of physicists who just follow each other down the wrong path when it comes to relativity and who render themselves blind to the most obvious contradictions and glaring faults in their pet theories, such as the event-meshing failures produced by all Spacetime models: [magicschoolbook.com] . They allow their beliefs to override reason every time. It's trivial to disprove Einstein's theories and it can be done in lots of different ways, but there's a powerful brainwashing system in place which messes with the minds of almost everyone who is taught relativity in universities, and 99% of the people who end up being highly qualified in that field are unable to correct their faulty beliefs, and no amount of mathematical proof that they're wrong has any impact on them.

I've never had kids, so I may not be the best to answer this. However I am an uncle to many. and what Neil describes here is almost exactly how I relate, and have related the the younger ones. IMHO, I was able to somewhat grow up to these ideas and ideals myself, so I get it. And to be honest, in my case, as well as others, has worked rather well. These two vids speak volumes.

If kids have questions, redirect the questions back to them. “Why do you think people believe that?” , “What do you think might have happened?”, etc. Let them process information without handing them answers (or our own opinions). Help them explore ideas.

Talk to your kid a lot, and like a human being, not "just a kid." Don't lecture. Listen as much as talk, and invite them to talk about their social experiences, which can make great case study example for talking about sociology and socially constructed beliefs. I guarantee religion will come up sometimes, as our kids will encounter it in peers and even teachers. Talk about what you believe and why, but don't claim yours is the ONLY perspective. DO teach by example the importance of backing up opinion....No, BASING your opinion on sound facts, not wishful thinking, myths, or conspiracy theory.
And be willing to discuss thoughts on why religion appeals to so many.

30 years ago, I might have said "limit screen time." In today's world, that is not only nearly impossible, but also a double edged sword. Schools teach with screens. Screens are the biggest source of knowledge by a mile, but both true and false information. Just like advertising, unless you and your kid live in a cave, policing screentime will be increasingly an uphill and losing battle the older they get. Limit screen time for the very young, Under school age. But teach kids to be computer-savy... To QUESTION what they see. We have to teach them to be critical thinkers about the online world. We cannot do that by sheltering them from it.

Teach a kid from a young age not to just believe what they're told or what they read or even see but to question everything and determine truthfulness through critical examination and to demand proof and evidence. You can even use religion as an example.

If they do that then they can have a cookie.

Send them out into the world and let them explore. Let them read everything they like, watch everything as long they can discuss it with you. Me and my darling kids learned and talked about everything. 3 out of 3 all graduates, all atheists.

Teach them how to read and write BEFORE they start the public schools.
Impress upon them that anything they want to learn about can be learned from BOOKS.
Buy them BOOKS, as well as toys.
Introduce them to the LIBRARY, and how to use it.
In no time at all,they will be formulating their own opinions.

This question can be answered with one word: Education. I remember when I was teaching math and science a girl student asked me: Oh, Mr. G. what do we have to learn this stuff for? I told her math teaches you how to analyze information. If some preacher starts talking about angels, you answer, OK, that's fine. What's it look like? Let me see one.

There are lots of things you can do. Some of my favorite ones that I've done with my own kids and grandkids are home science projects. Even really simple ones for young children are good for that. Create a problem, work out the solution with evidence and facts and complete to success. Example:

The experiment to show how oil and water don't mix. Let the kids help gather the ingredients, do the experiment, talk about how the evidence proves the hypothesis. Discuss how "evidence" is critical to truth and how myths and old wives tales use to be considered truth until the methodology of science and discovery became known.

Also, I use things they are interested in, like action heros, to talk about magic and the difference between reality and fantasy. Many times they'll make a statement and I'll challenge them to "prove it" if they can't then we make it a project to either prove or disprove their statement. As we go through the steps we are not only learning the information but also the process of skepticism and discovery. I make it a game and we always have fun. We do some sort of science every visit, from coke & mentos in the driveway to creating a vortex (simulated tornado) in 2 joined pop bottles. We've always done this.

When kids ask questions, help them think through the answer. "Why do you ask?" is a great start.

When my daughter Claire was four, we rented a house on the Pacific Ocean beach in Oregon for a week. I wrote in my journal:

Today Claire wore us down with her constant questions. After dinner, we walked down to the beach.

"Why are people walking on the beach?" Claire asked.

"Why do you ask?" I replied.

"Because this is our beach."

"Claire, think about it," I said gently. "Are there other houses next to ours?" She nodded.
.
"Do people live in those houses?" Another nod.

"Since there are other houses here with people living in them, don't you think that they might enjoy walking on the beach, too?"

Later, Terry praised me for that response. "You're teaching Claire how to think things through," he said.

The cardinal rule - there is NO one size fits all education. Use a multitude of styles.

I can only speak for myself and my upbringing.

I asked a question I was told to go look it up in the encyclopedia.

My dad (construction) brought home calculus, geometry and algebra problems from the job site every night and had me solve them.

You have to teach them to learn, then they will.

I think it depends on the age, but once they start asking the question "Why", it's on.

Once it's less "do this" or "I want" and changes to "Why", then you should engage them in conversations that make them think about the questions that they ask. If a kid asks why the sky is blue, ask them why they think it is. If they say they don't know or come up with something silly, outlandish or way off the mark, talk them through why they thought what they thought and why they started thinking about it in the first place. Then take them to where the right answer is and tell them why it's good reliable source material.

I found the best way to teach my daughter how to think was to make her think and then question how and why she came up with the answers she did. I found it more productive to teach her how to think about the questions that she brought to me instead of just answering them. Or I would give her a project so that she could figure out how to find the answer on her own or with my help allowing me to follow what she'd learned and how she's using it. Eventually this led to her doing some preliminary research and then coming to me asking, "Does this make sense" instead of just "why". Eventually she wanted to test her epistemology and get the "truth" instead of just an answer that suited her.

It helped quite a bit that we home schooled our daughter, so we were totally in charge of define how she developed information sources and interpreted the data therein.

I always make a point to address the common sense and emphasize more so when a mistake is made. I try to avoid philosophy like politics because modern politics is more like a mamby pamby game than like genuine politics blueprinted by the Greeks.

For controversial issues, like religion, I used to explain that some people think this... and some people think that... and I'd say which way I lean and why, though I didn't tell them which way to believe.

I also taught them to question authority sometimes. In one silly example, when my daughter was 3 years old, her dad and baby brother were sitting on the couch. When she tried to climb up on the couch to snuggle with them, her dad joked that "This is the boy's couch, no girls allowed!" so of course she came crying to me in the kitchen about it. I told her to go in and tell Daddy "That's discrimination!" and so she did (at 3 years old!) and it worked. She got to sit on the couch as an equal family member. Just silly things like that taught her to stand up for herself if she felt slighted or saw something unfair.

When my daughter was in first grade, her teacher asked each student to write down what they were thankful to God for during a Thanksgiving assignment. My daughter said "Nothing" explaining to her teacher, "I don't believe in God" which prompted a phone call from her teacher saying our daughter was "insubordinate." We had to go in to the principal's office to voice our concern that our daughter was being asked to participate in a religious assignment at a public school. -- This was not the last trip into the principal's office we took for similar "offenses" over the years, haha!

Show em how to use a hammer! But don't get any nails. That would be dangerous.

Beat the crap out of them! Just kidding.

riddles and puzzles.

One of the best things I did as a parent was to watch TV with my kids and point out how commericals would make assertions without support. My kids naturally look for evidence, assertions, the support for an assertion, citations, etc.

I'm a little unorthodox. Children often use their parents to figure things out. However, doing too much of this trains your child to trust everything you say. I resist the urge to answer questions and will often mislead them, at least temporarily, just to see what their critical response will be. If they react with a critical response then I know they have reasoned through my answer and correctly rejected it or at least paused long enough to ask a follow up question. I don't want them to be in the habit of believing adults, just hearing us. The fact they're asking me is enough. But by giving them both true and error their minds are being conditioned to consume the same thing from the general public and that's when this skill is more necessary. It's not enough for me to tell them that people lie and make up things and believe things that aren't real or untrue. I want them to be conditioned and trained from young ages to be able to handle conflicting the difference between fiction and fact.

I'd start out with math and science. No so much for the actual workings of the problem but to show them that complex problems can sometimes be hard to PROVE! It takes serious thinking about the issue... But you also want them to see the religious side of things to see how they differ. IMHO, you shouldn't push your child either way. However... If you were to show them some equations....

Science - X + Y = Z

VS

Religion

Rumor + hope = Faith (Or substitute anything else in here that is unproven or lack strategic measure)

This is how my parents did it with me. They wanted me to see and know both sides. You want your child to know about religion as they will have to discuss it during their lifetime... Perhaps just not follow it blindly!

My son 16 and I talk a lot. From Different ends of the spectrum.
Regarding social media, outside influences and modern trends, I tell him this must all be put into historical perspective. So think it through, don't panic, don't buy what people are selling.

Geometry

What age are your kids? When they are ready, help them to understand the principles of logic, which is the foundation of critical thinking. We use our logical framework to tell what is true and what is not. Teach them about the classic fallacies, which are some of the best tools to keep us from buying into irrational ideas. As soon as they understand that many of the people around them accept flawed ideas due to flawed reasoning, they will be more skeptical of ideas, even when they are presented by people they know, like and respect, reserving judgment until they see compelling evidence for or against said ideas.

I found being critical worked, doubly well when criticizing ‘advertisement,’ as I’d tell my kids, ‘was tricking us into buying something we don’t need.’ Seems in our PC police state, most have become fearful of criticizing anything. Do it, and they will follow. Ignore it, and they will follow anything ~