In middle school we used to build catapults and see who's would sling the farthest. How I would teach someone to make a catapult is:
Get the supplies-glue, popsicle sticks, rubber bands, etc.
Build a base with popsicle sticks
Build the frame/supporters with popsicle sticks on top of the base to support it
Drill side holes
Drill arm holes
Get a rubber band or spoon or rope and attach it to the popsicle sticks
Put a ball on the spoon
Crank it and watch it soar!