Most difficult puzzles are not impossible. They are just too large to solve all at once. Making the problem small is usually the fastest way to move again.
Start with the strongest clue
Find the fact that limits the answer the most. If one clue narrows things down, use it first and stop trying to think about every possible option at once.
Write down what is certain
Clear facts are easier to work with than vague guesses. If a detail is definitely true, keep it visible and use it as your base.
Look for the pattern
Many levels repeat a rule. If you see the pattern early, you can often solve the rest in a few moves instead of many guesses.
Try the simple answer first
The basic explanation is often correct. Before you build a complicated theory, check whether the straightforward answer fits the clue.
Use a hint as a nudge
A hint should help you get back on track, not replace your thinking. Use it when the block is real and then finish the logic yourself.
Calm thinking usually works better than rushing. Slow down enough to see the clue and the answer gets easier.