Having cycled my way through the Bain Chess Tactics for Students problem set once, I've turned my attention to a once-through of Reinfeld's 1001 Brilliant Ways to Checkmate. The recurring lesson is that visualizing basic checkmate patterns is the key to finding the right moves. Take this position (#76 White to Move) from the book:
Can you find the right moves? Check for the solution and more below the fold.
[FEN "6rk/1q1n1prp/p3pN1Q/1p1b4/6R1/6P1/PP2PP1P/3R2K1 w - - 0 1"]
1. Qxh7+ ! Rxh7 2. Rxg8# 1-0
Knowing that a rook can give mate on g8 or h7 (a basic pattern), it follows that the sacrifice Qxh7 forces open access to the mating square.
A good book for learning the basic checkmate patterns is Renaud and Kahn's The Art of the Checkmate (descriptive notation). This pattern from Chapter 22 is called the Arabian mate, because the Knight, Rook, and King have not changed their movements since the rule set in place before the game was introduced to Europe, according to the authors. The same checkmate pattern rates 3rd in a list of 50 in How to Beat Your Dad at Chess by Murray Chandler. This is also a great book for learning the basic patterns. Just ignore the title and colorful artwork on the cover, this book is about serious chess!
Now some advice will tell you not to spend too much time on checkmate problems, and I find some degree of truth in that. But aside from the number of games that involve such checkmates, remember too that many checkmate patterns appear in the notes, that is to say that the threat of a checkmate is often the basis of tactics in a game, even though the checkmate may never be played. And of course, learning the patterns not only provides ammunition for attacking your opponent, but a thorough knowledge is also a prudent self-defense.