I love catapults. They're my thing. I also like origami. Therefore, origami catapult. It took quite a while to brainstorm this, but then I had a breakthrough at a girl scout event. Ever since then, I have made catapults when I was bored. In that time, I feel that I have perfected the catapult formula. The key things to do the following:

Use thick paper. It has more bounce.
No squishing. Once it is squished, it will not work.
Hold tightly. If you don't grip the bottom, the whole thing flips upwards.
DO NOT USE IT TO ANNOY PEOPLE. You don't want to get hit with tiny paper balls, and neither does anyone else.

Let's get started!

Step 1: Supplies

Index card
Scissors

Step 2: Squareify!

Fold your index card so that it makes a 45º right triangle. Then fold the hangover down. Unfold, and cut off the hangover so you have a perfect square.

Step 3: Make a Square Base

Fold the square diagonally both ways so you have an X across the paper. Flip over and fold in half both ways. Flatten to a square base. Flip.

Step 4: Fold Points to the Center

Fold the outside point of the square to the center line. Repeat on the other side. Unfold.

Step 5: Flatten

Open up the first layer of the square and fold in along the pre-made creases. Then fold the inside of that fold to the edge. Repeat on other side and flatten.

Step 6: Fold Points to the Center Again.

Fold the outside point of the square to the center line. Repeat on the other side. Unfold.

Step 7: Finish

Open the first layer of the square. Bring the edges up to the top.

Step 8: Video

If you get confused at any part, I suggest watching this video. Seeing it actually happen can work wonders.

Step 9: LAUNCH!

YAY! Now you can launch paper! I suggest using the leftover part of the index card for your ammunition. Just scrunch it up into a little ball. Here are some tips to make your launching better:

Use lightweight ammo. The paper is only paper.
Press on the bottom of the catapult.
Go back far.
It actually goes pretty far if you do it right. I have launched paper halfway across my classroom in school and hit people in the head by accident.

Also, it can work as a bookmark. So you can launch paper from your books. And the video is in slow motion.

Go forth and launch!