If using a plastic hanger, then all you need to do is place the object being launched on the part of the hanger with the most area, hold it, pull back, and release. If your hanger doesn't have a part with a lot of area, then wrap an end in tape until the desirable area is reached.
Step 3: How to: Metal
If you use a metal hanger, more than likely, you will need to wrap it in tape to give it some area. When you feel it is good enough to launch, the follow the easy steps in step 2.
There you have it. The world's easiest, and cheapest hand-held catapult. Enjoy!!!