When folks encounter a video game challenge that requires a high degree of mechanical skills, like a boss fight in a Devil May Cry or Bayonetta, I find that they are generally more willing to try and try again or even maybe admit they are not skilled enough to do it. When it comes to puzzles though... I've observed that many players do not like the idea they couldn't solve them. They will call them bullshit. "How was I supposed to figure this out?" Puzzles test your logic reasoning skill. In our society we have a tendency to associate that particular skill with the completely fake concept of intelligence. So when you can't solve something, it's like being told to your face that you're not very smart. Just go on the comments of a solution video for any of the trickier Baba is You puzzles. You'll find plenty of people complaining it was unintuitive or the game made them feel stupid.
But here's the thing. I firmly believe puzzle solving has nothing to do with "intelligence". It's a skill, and like any other skills, it can be learned and honed with a lot of practice. No one expects a player new to fighting games to be able to win a tournament without first learning and practicing the fundamentals. Why should it be any different for logic puzzles?
Here are a few things that personally helped my puzzle solving skills:
Look up tutorials on how to solve classic puzzles
This might sound obvious but I think a lot of people assume that, because puzzles are a test of logic, they should not need any help to solve them. Seeking help would be a sign that they are not intelligent enough to figure it out on their own. A big example is Sliding Tile puzzles. You see them in a lot of video games, even ones that aren't focused on puzzle solving, because they're relatively easy to implement. Players hate them though! It seems to be the general consensus that these puzzles are terrible, tedious and obnoxious. I think the main reason people hate these is because they do not know how to solve them efficiently and I have yet to see a single video games actually teach you how. So they flail the pieces around randomly until it solves itself. Doing that feels very unsatisfying. There is however a simple method you can use that always works.
Like seriously, just watch this tutorial. It's timestamped at the explanation. After watching that, you will never struggle with simple sliding tile puzzles again, I guarantee it. You might even start appreciating games that take the concept much further like Cogs!.
There are established methods to solve every classic puzzle, you don't have to reinvent the wheel. Look up how to solve a Rubik's Cube or a Tower of Hanoi or a Nonogram. Even if you don't generally play games featuring these types of puzzles, just learning the methods will train your mind to think within that kind of logic.
Take notes
And I don't just mean the occasional hint and key phrases the game gives you. I mean write down all the rules of the puzzle environment as you observe and understand them. Test these rules regularly to see if you did not misunderstand them. Whenever you're stuck, revisit your notes and try to see if you forgot about an obtuse interaction that is rarely used. Taking notes is fun! Doddle the characters and the puzzle elements! Make the notebook feel cozy! You'll get a really cool souvenir you can show other people later when you're done.
An example I like to mention: some years ago, let's player SuperGreatFriend did a blind playthrough of The Witness. At the end of each video he writes down everything he learned about the rules of the game. Fairly often he would get stuck on a puzzle because he forgot about a specific interaction or made an incorrect assumption. Yet he manages to complete the game in the end by reading through his notes between each session.
Work your way backward from the end
Often, tricky puzzles place you in a starting position with a lot of different possibilities. Sometimes one component of the puzzle seems central to the solution but then turns out to be a red herring. It can be hard to discern what is the correct approach from there. If you start at the end point and establish every step that must be done to get there you can get a better idea of what the puzzle wants from you. Try Rubber Ducking the puzzle. Explain verbally to yourself out loud what the goal is, what the problem is and what you need to do to get there. You might hit on the solution simply by describing the problem.
Solve previous puzzles again
It might sound useless and tedious. Why would I go back to puzzles I've already solved? Do not dismiss that advice. A well designed puzzle game generally tries to teach you something about how its components interact every new puzzle. Reviewing older puzzles can remind you of mechanics you forgot about. Write down the lesson that the puzzles taught you. The absolute worst thing that can happen in a puzzle game is if you solve it without understanding why it worked. If you struggled with a puzzle, do it again. Try to optimize the solution. Eliminate all the extra moves. Can you summarize the method to solve it with the absolute minimum amount of instructions necessary? You might learn something new doing this. It's also just good practice to re-do older puzzles. It helps internalize all the different movements you need to use and you'll get faster each time.
Take breaks when you get stuck
Seriously. I know this is a cliché advice but it's absolutely true. Just put the game down and do something else. Come back to it the next day after a full sleep. It's very easy to get stuck on a puzzle because you are convinced it must be solved a specific way and are currently unable to consider a different approach. Letting the puzzle leave your head and coming back to it later with a fresh mind will help you open up to other possibilities.
Feel free to add your own methods of solving difficult puzzles!
