Summarize:

Place your middle finger on the right side of the ball and your index finger right beside it. The most important part of the grip here is that your middle finger is on the inside of the seam. By having your middle finger on the inside of the seam, it allows you to flick downwards later on when you release the ball. This is what actually creates the spin. Your thumb and other fingers should be on the bottom of the ball and from the side your hand will look like a horseshoe around the ball. This will prepare you to engage in the weight shift necessary to get maximum power on the throw. Your left leg should be bent and your knee should be brought towards your chest. These instructions are for a right-handed pitcher. If you're a left-handed pitcher, lean back on your left leg and raise your right leg instead. This is the first part of the weight transfer which helps you maximize the velocity and spin of the pitch. Your hips also need to open up from the coiled position they were in before. The chain of motion should go as follows: left leg first, followed by opening up of the hips, followed by your pitching arm snapping forwards and finishing down by your opposite hip. This process incorporates your entire body into the pitch. When you're throwing at game speed, every pitch should have maximum effort in it. The only difference between a fastball and a curveball is where you are applying the spin. Try practicing this chain of motion at a reduced speed before you work up to full pace. This is the single most important contributing factor to actually creating the curve. When you do this, you create the forward spin on the ball that makes the ball drop and curve in the air. It takes a lot of practice to get this motion right but once you get it, the results will be very clear. The goal of this type of curveball is to entice the batter into swinging at the ball early to elicit a strike. To do this, you need to throw the ball so it looks as though it is coming into the strike zone and then curves downwards at the end. This is something that obviously takes a lot of practice to master but before you throw at full speed, aim to be able to do this with about 80% accuracy.
Grip the baseball as you would with a 2-seam fastball. Load up by leaning back on your right leg and lifting your left leg in the air. Snap your left leg forward and plant it on the ground. Pull your arm forward as you snap your leg forward/downward. Flick your fingers down over the front of the seam when you release. Aim to throw the ball so it finishes underneath the strike-zone.