Note: I've written this instructible in the first person, because it is far from an authoritative set of instructions, but merely an account of how we went about building a trebuchet, compiled to help others create their own.
Step 1: Theory
The trebuchet consists of a base and a swinging arm. On one end of the arm (the much longer end, to gain mechanical advantage) is a sling in which the projectile to be fired is loaded. On the other end is a heavy counterweight.
The sling is a very clever edition to the trebuchet. It acts as an extention to the arm, without the added bulk of extra timber. When ready to fire, the sling is attached at both ends to the arm, but as the arm swings around, one end of the sling detaches (when it detaches is adjustable, to account for differently weighted missiles) and opens out to allow the projectile to be thrown free.
Most of the "Insensible" is made of recycled wood, with a steel crossbar (the axle for the arm), and concrete counterweight - 120kg.