The purpose of this post is to increase your tactics rating.
Most chess puzzle solutions fall within the "quiescence search" of game programming - forced sequences of captures, checks, threats of mate in 1 and attacks on an unguarded piece or a piece of greater value - what Lasker called the "violent" moves.
Diagram 1
For instance Diagram 1 is taken from Fred Reinfeld's 1001 Brilliant Sacrifices and Combinations, Diagram 436, The Overworked Piece.
If this came to you out of context, following this method you would find that the solution 1.Re8 is a threat to win the queen, then then you would notice that both captures of the Rook allow mate in 1 or mate in 2.
The next position is Diagram 100 from the book Tal's Winning Chess Combinations by Mikhail Tal and Victor Khenkin.
Diagram 2
Next is Ljubojevic vs Durao, 1974, shown on page 169 of Tal's book:
Diagram 3
The quiescence search also solves most endgame studies, even this one by Troitsky:
Diagram 4
But how do you see a move like 5.Rd4 without moving the pieces? This is a topic for a coming post on visualization.