Construction is snap-together!
Feed an elastic band through each of the bores on the side braces. Tie it through the bore on each winding key. Slip the end of the throwing arm through the rubber bands. Repeat with as many rubber bands as will fit through the holes. Needlenose pliers will help here.
Twist each key 10 times and then lock it in place by inserting the locking tenons into the square holes on the side braces. The more twists, the more launching power you'll have. Careful, pennies can sting, especially if you take an Abe to the forehead.
Flagrant stagecraft alert: the clever-eyed among you will note the use of black electrical tape to keep the throwing arm cocked for the photo.
If you need a target, try the Seej basic bloxen: http://www.thingiverse.com/thing:23620
UPDATE 6/2/12! Thanks to Thingiverse user Wauter for pointing out some geometry problems in the winding key and side braces. These have been addressed in zheng3_catapult_clean.zip
Seej is a tabletop wargame based around 3D printing. Check out http://www.s33j.net for rules and more information.
You can change the payload's arc by raising the front of the catapult. Have fun storming the castle!