There are many ways to throw a frisbee, here are some of them.
The 3 most commonly used throws in Ultimate:
The easiest and probably most commonly used throw. Put four fingers in the cup of the disc with your thumb on top. If you are a righty you would stand straight up, twist to the left, bend your wrist and elbow in front of you so they are in front of the disc. Then undo all of that in one steady motion releasing the disc. Try to keep the disc as level as possible and to give it spin. Most of the spin comes from bending your wrist then snapping it.
A flick is easy, but takes some practice and commitment. Put 2 fingers under the disc and your thumb on top. Throw as if you were trying to skip a flat rock on water. Keep the disc parallel with the ground. The key element to the flick throw is the spin you put on the disc. Do this by pulling your wrist as far back as it will go and snapping it forward while bringing your arm through the motion.
Very useful when the time is right. To throw a hammer simply pretend like you are throwing an axe. First, hold the disc with your pointer and middle finger on the inner side of the disc, your thumb on the outside (same as a flick). The top of the disc should be facing your left side. Tilt the top of the disc slightly to the left side to give it an angle. Pull back and release the disc when it gets even with your forehead, keep your elbow bent at all times. If done right the disc should start out tilted and slowly turn upside-down. The disc should land completely upside down on its face because it makes it more predictable and easier to catch for you teammate.