This is the third installment of four in the Beginners' Chess Strategy Series. I'm here to help those still learning the game by outlining a few examples of specific techniques that help thin out enemy ranks and restrict opponents' choices.
As was evident in Part 1, a multi-pronged offense is often a more advisable approach than simply going through the motions of single attacks, which are especially avoidable during the flexible, unpredictable opening and mid-game phases. Unlike the fork, however, the following strategy pits two pieces versus two in a way that often alarms opponents, simply because it doesn't occur to them that their king could be put in check so subversively: the discovered attack.
In the image shown here, it's White move, and he intends to move the knight at D5 to F4. This executes two simultaneous attacks: the knight not only then threatens the Black rook at H3, but has cleared a path for the bishop at F7 to put the Black king in check! Naturally, Black must then move the king, leaving his or her rook a sitting duck.
Say instead that it's currently Black's turn. Which potential target does Black move, the king or the rook? It depends on to where they'd each move. It's useless for Black to attack White's defended bishop, and threatening the knight would merely prompt an easy move out of the way and thus still leaves Black's king in check the next turn. If you see a discovered attack coming, just as suggested in Part 2, you can often stall for time by putting the opponent's king in check (such as if the rook at H3 moved to H8).
Or, on this simple board, there's plenty of room for Black's king to extract himself from the dangeorus situation; most highly advised is a move to B2 or A3, since A2 and C4 would leave the king on the same threatened diagonal, and A4 or C2 could prompt a subsequent check (thus restricting move choice greatly) from White's knight. Finally, the King could of course not move to C3 or B4, because the Knight currently has those spaces covered, and Black would be stepping into check. With more pieces present, the prospect of an escape might be moot anyhow.
Try using the discovered attack. It takes a little bit of foresight to setup, but can be devastating if executed correctly. Be sure to also read Beginners' Chess Strategy Series, Part 4 -- the endgame. Have fun, and never lose that competitive spirit!