How To Throw a Frisbee
There are four common ways to throw a Frisbee: Backhand, "The Flick", "The Hammer" and "The Chicken Wing". Backhand appears to be the most common and easiest to learn. It is good for keeping the flight of a frisbee level and straight, though it is not hard to make it turn to one side or the other by simply canting the disc in the opposite direction that you want it to curve to.
The Flick is where you hold the frisbee with your index and middle finger under the disc and your thumb on the outside edge of the frisbee. This method is very easy to curve and is a more powerful throw than the backhand. You can make this throw fly level as well but you have to keep it low because if the way your hands hold the disc it is hard to give it a lot of force the higher you throw it from relative to your height.
The Hammer is a variant of the flick meaning it is for long range passes, with starting and ending point almost straight to each other, but the frisbee does not travel straight. You hold the disc the same way as you did for the flick, but instead of holding it to your side you will be bringing it from behind your head and releasing over your head depending on how far you want it to go and how high you want it to get.
Last but certainly not least is the Chicken Wing. I would describe this one as almost the inversion of the backhand. Instead of having your thumb on top of the frisbee, it will be under the frisbee on the inside, and the rest of your fingers over top of the frisbee with the disc out to one side of your body (like with the flick). This one curves mostly depending one what side of your body (which hand) you throw it from, though it is not too hard to get it to fly straight as well. Here is a video showing how to throw "The Chicken Wing".