Please excuse the number of steps. It is really easy and can be made within an hour and from bits lying around the office, hence very cheaply.
Step 1: The tools and materials list
1 pair of pliers (needle nose would be best, where available)
1 pair of scissors (yay for scissors)
Corrugated card (approx 6"X6")
Ballast (I used a bunch of batteries from our recycling box)
Step 3: Now shape them
At the other end, make a dog leg. Try to make it on the same plane/axis as the eyelet.
EDIT: Ignore the dogleg. Instead bend approximately 1/2" of the non-eyeleted end at right angles (90 degrees) to the eyelet. All will become clear very soon.
Step 4: The axle
Step 5: The arm
Make a small hook at the other end.
Step 6: The trigger
EDIT: See the adjustment I made to the firing mechanism in the final step. It works so much better.
Step 8: Assembling the parts
Step 9: The base
EDIT: Cut the card to 3"X6" with the grain of the corrugation laying along the 3" distance. Mark the center line along the 6" distance and two lines 3" apart at right angles to the center line.
Step 10: The base (cont)
EDIT: The new style supports from step 3 don't get pushed through the card as shown here. Instead, insert them into the raw edge of the card. You don't have to worry about the angles of the doglegs being incorrect, and these will be much easier to secure in position with Cellotape.
Step 11: Mounting the axle
After that, tape between the legs to make an A-frame and then from there to the sides of the base to prevent side to side motion
Step 12: Mounting the trigger
The other end of the trigger needs to run in a slit so that it can slide back and forth. Don't make the slit too long or else you risk the trigger being pulled out.
EDIT: See the last step for attaching the improved version.
Step 13: The ballast
Use the rubber band to attach a whole bunch more batteries around the one with the hook
When they're all assembled and hooked on the arm make sure the ballast is not touching the base.
Step 14: The ammo
Wrap it around a couple of times and then smoosh the Blu-tac into a ball.
The extra string inside will allow you some length experimentation to gain maximum distance when firing. A good length is about two thirds the distance from the hook to the axle along the arm.
Step 15: Finishing up
Position the ammo on the center line and at full extention of the string.
Aim and fire by pulling the loop on the trigger towards you. CAUTION!! The arm moves fast and has a sharp little hook on it. Don't use near your eyes. Also, this isn't the most acurate piece of equipment ever designed. Just because you're aiming it forward doesn't mean the Blu-tac is going that direction. Make this at your own risk. And make sure your laces are tied. And no running with scissors.
Step 16: Extras
Step 17: Release pin modification
I rotated the release pin 90 degrees so that now instead of drawing back like a bolt, it's hinged and rolls back off the hook of the arm. You launch by pulling back on the lever.
Very simple and you can use the original pin, though it may need some reshaping. Just make sure that it's placed far enough foward to release the hook and that it doesn't snag the ammo on it's journey past.