As far as I can tell, exhaustive search tends to be the solution.
I still remember the magic of discovering cryptic crosswords. Regular crossword puzzles are fine but cryptics are their own sort of fun.
While some adventure games do rely on so-called "moon logic", the solutions are pretty much never completely arbitrary but rather require you to think out of the box, take descriptions/names/etc. literally even when that would not make sense in the real world, always look for possible puns or other jokes. Play enough of them and you will quickly get an intuition for these puzzles.
Of course, there are P&C adventures that go for more realistic puzzles if that is what you prefer. You'll still need a sense for puzzles though and won't always immediately know what to try next.
Personally though, I always had the most fun with these as a bunch of pre-teen friends standing around the computer throwing out ideas. I really struggle to play a lot of puzzle games now that I'm older since I miss that dynamic, and tend to stick to more straightforward ones like Tametsi/Hexcells (think Sudoku/Minesweeper).
This lets you get hints for the part you are stuck on without spoiling other puzzles or story bits.
Can't recall many without reaching out for a hint here or there. There's always things in these types of games that are totally illogical. I'm suspect of anyone who says they beat these things with zero help at all as IME it's down to myopia in writing/design in most cases.