Here is a PDF of the Instructable that includes all the secondary images and annotations.
Here is a video that shows how it works.
Another video of assembly to help if you are having trouble working out some of the steps.
If you want to build one and don't care as much about the appearance you can try the quicker and easier method.
Step 1: Things You'll Need
Small rubber bands
Something heavy and flat (like a large book)
Cardapult design (attached in following steps)
Other stuff that may come in handy:
Something heavy and hard (like a hammer)
For the paper I had a hard time finding anything thick enough locally except for the perforated sheets for DIY business cards. These will work, but alignment is more difficult since the edge of the card is already made. You'll need something about .012" or thicker. Which corresponds to 90 lb Cover and 140 lb Index (card stock). If you are just making these for fun then old folders or thin cardboard product packaging will work great as well.
I tried a few different glues and the best I found for these purposes was an Elmer's Craft Bond Glue Pen