For your regular curveballs, you jam the ball between your middle finger (usually on the seam) and your thumb. With a stiff wrist, most pitchers concentrate on pulling down on the ball to create the downward, vertical spin that makes a curveball drop.
Standard: Index finger rests lightly on the ball without applying pressure.
Crossover: Index finger crosses over and rest atop the middle finger.
Pointer: Index finger points straight up, so that it is not resting on top of the ball.
Knuckle Curve: Commonly thought of as a different pitch, the knuckle-curve is merely a different placement of the index finger, in which the second-digit knuckle of the index finger rests on the ball.
Slow motion example of a curveball in flight:
Al Leiter does a great job of explaining the basics of a really effective curveball. This is a must watch.
MLB pitcher Adam Wainwright does an awesome job explaining how he grips and throws his curveball.
Now you need to go out and practice this over and over and over. One great drill is throwing the ball into a bucket.