The slider is an effective pitch because while it's not as fast as a fastball, it's faster than a curveball, breaks laterally, and is relatively easy to throw without putting too much strain on the elbow or wrist. To throw a slider, grip the baseball with the standard grip for a four-seam fastball*. Now, WITHOUT MOVING YOUR THUMB, slide your top fingers across the ball towards your body until your index finger is across the seam. You should feel a bit of strain on your middle finger, almost as though the ball is trying to squirt out to the side. This is OK. To throw the slider, throw it exactly the same way you would throw a fastball. The resulting pitch should break down and to the left if you're a lefty, and down and to the right if you're a righty.
* If you are unsure how to grip a four-seam fastball, do the following: Look directly at the ball, and rotate it until the stitches form a "C" (Note: if you're a lefty, you want the "C" to be backwards.) Your middle and index fingers will go straight down the middle of the ball, with the tips of those fingers resting on the top stitch. Your thumb goes underneath the ball, with the tip of the thumb holding on to the nearest bottom seam. No other part of the hand should touch the ball. This is the four-seam fastball grip.