This posting will show you the simple step by step process to making a small catapult (as shown below) out of mostly Popsicle sticks. Here is also a link to my video showing how to make the catapult step by step: http://www.youtube.com/watch?v=BuNfdv0yFTg
Start by grouping 5 or 6 Popsicle sticks together with an elastic band
Attach one Popsicle stick in the center of the bundle, by wrapping them together with a slightly larger elastic band
Glue 3 Popsicle sticks on the back to form a base as shown below
Glue a bottle cap to the top of the arm to carry the projectile
Test out the catapult by pulling it back and releasing. If you want to get more distance attach an elastic band from the back of the base to the bottom of the arm.