- look at checks, captures, and threats for both white and black, paying special attention to any forcing moves
- using that info create a list of candidate moves
- step through each candidate move, reassess checks, captures, and threats for the next move, and repeat until the best solution seems obvious (puzzles aren’t usually too vague from what I’ve seen)
So it’s like working your way down the branches of a tree.
Hope that helps some.
Obviously “Improve Your Position” is the general goal, but it’s hard to see what this desired improvement looks like. Quite often I’ll end up taking the hint or asking for the solution, and I think “Ok... so why would I do that?”