A trebuchet is distinct from other forms of catapults in that a trebuchet has a long, pivoted beam, with the pivot placed so that one end is much longer than the other. The short end is pulled down (by a weight in counter-weighted trebuchets, by a team of human pullers in a traction trebuchet), causing the long end to rise quickly. A sling is attached to the end of the long end; one end of the sling is tied to the long end while the other is one a hook. The payload is held in the middle of the sling (e.g. with a bucket). When the long end rises, the sling whips over, releases itself at the hooked end, and hurls its payload at great velocity.

You can see how the trebuchet works by clicking here. Note that the illustrations on that page are looking at the trebuchet from the right side, whereas my photo is from the left (gunner's) side.

The counter-weight is at the upper left of the short arm, and consists of a wooden box filled with lead. The trigger is of the Danish Medieval Center Trigger discussed here. You have to look closely for the bucket; it's just to the left of the center post.

Here's information about the trebuchet that flung a piano and a coffin on the TV series Northern Exposure.