This video illustrates the right way to throw a Frisbee. It is important to understand the arm movements. The natural way to throw a Frisbee is by swinging the arm in an arc, but that isn't the most efficient motion to use for throwing. Swinging in an arc and trying to throw in a straight line doesn't work for high level Ultimate throwing.
For the backhand throw, think about pulling a lawnmower cord - you pull it straight out. Also, throwing on one foot forces you to rely more on the arm action rather than the body. This gives you more power and control.
For a good forehand throw, use a whipping action similar to snapping a towel. You need the straight movement with the wrist snap at the end. The arm movement is one of the most important aspects of throwing.