I disagree with Calmeacham. I wouldn’t recommend that a beginning chess player study openings. (1) You’ll forget (most) everything without fairly constant study; (2) you won’t fully understand the ideas behind the opening systems and thus will be lost once you’re “out of book”; and (3) since your opponents likely won’t know anything about openings, you’ve got nothing to lose by not studying them in depth.
Instead, I’d recommend studying the endgame and tactics. Understanding the endgame is a boon because (1) you’ll learn how to use the various pieces more effectively independently, which will carry over to other elements of the game; and (2) you’ll learn to recognize a winning position and will know when to trade down. Unfortunately, most endgame books are boring and merely consist of exercises. Bruce Gandolfini does a halfway decent endgame course, but like many of its ilk, it’s boring. So perhaps studying tactics is the way to go; it’s fairly easy to pick up and drastically impacts your performance over the board. Note that I’m referring to “tactics” and not “strategy”: they’re sort of terms of art in the chess world. Tactics refers to sudden piece combinations, and are usually organized by motif: forks, pins, discoveries, skewers, and the like. Strategy is much more abstruse and difficult; really buckling down and learning is something that should wait until you’ve got a grip on recognizing and exploiting tactical positions, and avoiding giving your opponent opportunities to ruin your position with a well-timed knight fork. As far as a good tactics book goes, you’re in luck. Most are written for beginning-to-intermediate players, and thus aren’t all diagrams and notation. A good example of one that has a pretty decent amount of explanation and isn’t a terrible bore to read is Winning Chess Tactics, by IIRC Yasser Seirawan. (I may have spelled his name incorrectly.)
Another option is to skip the books and try computer resources. The Chessmaster series usually has a series of exercises and drills that purports to teach you at a somewhat superficial level all aspects of the game. The later versions even have master games that a player then analyzes for you, explaining why the players moved what where. There’s also rating exams to make you feel pathetic – but at least will help you figure out what to work on.
Best of luck!