How to throw dough, a basic step by step guide.
Make sure you have a dough that can stand up to being airborne. This means that you need a high gluten dough. You can throw wetter doughs as you get more experienced but they require much more precise hand placement and are much less forgiving.
Make sure your dough is fully risen with out being "blown". It should be elastic and soft to the touch.
Coat dough in flour. This step is necessary to allow free spinning on your hands and to get good, clean releases.
Create crust. You can use the method that daniel describes, you can use the Papa John's fold and tuck method, you can do it like this video, it doesn't matter as long as you end up with a piece of dough that is flat over the interior with a ridge going around the outside.
You should be comfortable with in-air hand stretching before you get to the actual throwing. This is when you place the dough on the backs of your hands, support it with your knuckles and stretch it out. This position is a great way to start a basic toss that won't rip your dough as you will be catching with the backs of your hands and not your fingers. You want to release the dough by having your right hand provide upward thrust as your left hand provides spin. This will provide a straight up toss that is very easy to catch.
The way to do the more advanced throws is learn to release from your finger tips. This involves having your fingers rest along the ridge that we made in step four. You can check out a quick tutorial starting at 2:17 on this video. Feel free to ignore the rest of it, but it was the best explanation I found online. Basically, you want the dough to hang in such a way as to allow you to impart spin and momentum with just one hand, while other is occasionally used as a stabilizer. This allows tricks like the roll and the through the legs and all the others.
Important tips that will help you be successful at learning this skill.
Cold dough is more elastic than warm dough. That means its terrible for pizza but great for practicing. It also resists puncture a little better, so less holes.
A damp kitchen towel has about the same aerodynamics as a piece of dough. It's what I used to train the guys at my restaurant on for extra practice, and it's way cheaper than one of those rubber doughs.
The dough should always be spinning in the air. If it's not, you aren't doing it right.
Throwing dough can result in a very thin middle. You want to make sure that you are stretching evenly and keeping an eye on that if you intend to use the dough for it's actual purpose of delicious pizza.
Practice, Practice! Throwing dough is a physical skill and you have to train your muscles a little to be good at it. It can be a little frustrating at first but stick with it, it's a lot of fun.
If you have any additional concerns leave a comment and I'll do my best answer them.