I decided to submit this instructable after the trebuchet was already built, mostly because I wasn't sure how it would turn out. But I took some pictures and have a few videos so you can get an idea of how it works and how it was put together.
One additional comment before we get started. I'm really not sure what the range of the trebuchet is, considering I cannot test it outdoors because of the weather. However, adjusting the range is pretty easy though: shorter sling yields earlier release; shorter boom tip yields earlier release.
Also, there are plenty of cool ways to rig up a trebuchet, this is just the way my roommate and I did it. Have fun and be sure to shoot as many projectiles indoors as you can (I recommend practice golf balls).
Step 1: The Five Major Components
Step 2: The Boom & Counterweight
In order to keep the boom from shaking apart from the counterweight we tried to add supports where we could. Ultimately seeking to eliminate twisting of the boom and side to side swaying of the counterweight. See the pictures for notes on the supports.
The distance the axle must span was also an important consideration: if too wide, supporting the boom may become difficult, if too narrow, the counterweight may not have enough room to shake side to side. Ideally the shaking of the counterweight would never be a problem, but in this world, ideal is simply fiction.