Here is a little case study about how I taught myself to throw a Frisbee left-handed (I am naturally right-handed). Perhaps it will help you approach similar endeavors of your own.

1. I decided to learn to throw left-handed. I chose to work on the backhand (the standard throw) first because it is simplest.
2. I broke it down into small motions by doing it slowly with my right hand and asking myself what each step in throwing was really doing. I found that I was crossing, pulling my arm back, moving the disc forward parallel to the ground with a smooth arm motion, and releasing with a strong flick of my wrist, pointing my hand in the direction I wanted the disc to go.
3. I practiced each step individually, especially the wrist-flicking and releasing / aiming steps.
4. I worked out other throws in addition to the backhand, such as the forehand, hammer, and gull-wing.
5. I worked on catching the disc with either hand as well.
6. I began introducing the throws into games I was playing when the games weren't too intense.
7. I've kept working at it and have found that across the last year I have begun to naturally throw with both hands rather than just my dominant hand.