There is only one real good way I have found to do puzzles.
#Megadungeon Project: Puzzle Implimentation
mighty juniper
So, I'll give you an example of a puzzle I made.
Circular room with dozens of openings in the walls, in which there is a mixture of hobgoblin skulls and elf hands, mummified. Among the various holes are also candle holders without candles that have long melted away. In the center of the room is a large statue of a foreboding hobgoblin warrior. Surrounding him are 5 large stone spears sticking out of the ground. As a last component, there are 5 colored orbs in the room in the little alcoves, each a different color, and each gives a different elemental sensation - heat, blown air, earthy smell, etc.
Stab a guess at the solution.
Here is my trick
I don't know the solution.
I just made the puzzle. The players get to figure out the solution. If it sounds reasonable, cool cool lets do it.
If I want, I'll have them roll dice to see if their character figured it out - this really is just "was this the solution or not" roll, really
The players will not fail to get thru this door, unless I want them to roll dice. They get the excitement of figuring out the puzzle, and discovering they were "right".
And usually, a solved puzzle is way way more interesting than one that does not get solved.
toxic lichen
If you want to make a megapuzzle, be prepared to give some hints for skill checks
you don't have to give them out immediately, but have them ready, because unless the solution is something that can be reasonably understood by a bunch of nerds.... it's just going to get frustrating
mighty juniper
So the thing is, the idea has to be reasonable and sound. "I do a voodoo dance and speak the name of the trees outside" doesn't cut it, it needs to make sense for the puzzle at hand. It's definitely not the Sphinx saying yes to every answer; the first answer that seems like a reasonable way to solve it and the player can back up with reasoning becomes the solution.
warped heath
I'd say the first thing is to set the expectation of the puzzles
I'd take a look at puzzle-themed games like Portal 2 to see how they set up their mechanics
they start with getting the player used to the core mechanic of their puzzles - for instance, Portals gets you started with the basics of using portals. Then over time expanding over that core mechanic.
Honkai: Star Rail has puzzle minigames, and they do something similar - set up the core mechanic of the puzzle, and then over time iterate on it.
If you have multiple puzzle types, consider using them as interlocking puzzles - one puzzle unlocks the piece of another puzzle, to unlock another puzzle.
That lattermost is, I think, key to framing it all back to the monster-slaying adventure slugfest that is 5e. It's a game that likes it's combat, and finding a way to interplay combat and puzzle in a consistent and interesting way should make it that the players are satisfied with the puzzles.