Puzzle toys are the enrichment item people are most skeptical about, and the skepticism is half earned. They do work. They also stop working, faster than the packaging suggests, and the reason is built into what a puzzle is.
The part that works
Working out how to get food out of something is real cognitive effort, and it produces the same settled dog afterward that a long sniffing session does. A dog who has spent fifteen minutes on a puzzle board usually goes and lies down, which is not what happens after fifteen minutes of fetch.
It also slows down eating, which matters for dogs who inhale a bowl in fifteen seconds, and it gives a dog something to succeed at. Watching a dog figure out a new layout and then do it faster the second time is a fairly clear sign that something worthwhile is going on.

The part that does not
A solved puzzle is no longer a puzzle. Most dogs crack a level one board within a couple of sessions, and then it is just a slightly awkward bowl. People read this as the dog getting bored of the toy. They are not bored of it, they have finished it.
The other honest limit is duration. A puzzle board buys you ten to twenty minutes, not an afternoon. Anything sold as keeping a dog busy for hours is either being optimistic or is so difficult your dog will give up on it.
How to keep one interesting
Change which compartments you bait. Costs nothing and resets most of the difficulty. Do not fill every one.
Change what goes in. A smellier reward makes an easy puzzle worth doing again.
Put it away. Two weeks in a cupboard and it comes back new. This works better than buying another one. It is the same principle behind rotating any enrichment toy.
Move up a level. Once sliders are easy, a board with a row of covers that slide on a turning disc, so the right move changes depending on where the disc is, is a genuine step up. The BorkBrain Puzzle is built around that idea, with compartments you can leave open while your dog learns and close as they get quicker.
How to teach a dog to use one
A lot of puzzle boards fail because the dog was shown the finished version. Put food in every compartment with every lid off and let them simply eat it, twice. They now believe this object contains food, which is the only thing they need to believe at the start.
Next time, cover half. Then all of them. If they stall and walks away, you have moved too fast, so go back a step. Dogs give up on puzzles that have been too hard once, and getting that interest back takes longer than doing it slowly in the first place.
Sit nearby the first few times. Encouragement helps, but do not solve it for them. The moment you lift the lid, you have taught them that staring at you is faster than working.
Choosing one that is not a waste of money
Look for a base that grips the floor. A board that slides into a corner turns into a shoving match and dogs give up on it. Look for pieces that cannot be swallowed and cannot be chewed off, and check how you are meant to clean it, because dried wet food in a compartment is unpleasant within a week.
Avoid boards with loose pegs small enough to swallow if your dog is the kind to try, and avoid anything where the moving part is a thin strip of plastic.

Puzzles are only one drive
This is where most people go wrong. Food puzzles satisfy problem solving and, to a degree, sniffing. They do nothing whatsoever for the chase instinct.
So a dog who finishes a puzzle and immediately brings you a ball is not being ungrateful, they have completed one activity and is asking for a different one. That drive needs something that moves. A ball that rolls away and comes back on its own covers it without a half hour of throwing, and the interactive balls vary in how predictable they are, which matters for dogs who solve things quickly.
Most households end up with one food toy and one moving toy, and that combination covers far more than two food toys ever will.
The free version
Before spending anything, test whether your dog is interested at all. Put treats in a muffin tin and cover each cup with a tennis ball. Roll kibble inside a towel. Put a handful in a cardboard box with crumpled paper on top.
If your dog works at those with real focus, a proper puzzle board is worth buying, because it goes several levels further and survives being washed. If they sniff once and walks off, they are probably a dog whose interest lies in chasing rather than solving, and you have saved yourself the money.