When: The Trebuchet was first used In China during the 4th century, during that time the romans were using aqueducts, roads, bridges and dams. Along with having an advanced waste disposal system borrowed from the minoans

What: their were many tools and machines used by people during the fourth century, a suprising example is a crane which were supposedly worked by treadwheel or crank. another example is the crank/lever and air and water pumps, along with an archimedes screw. their was also basic plumbling being employed using clay to create pipes for sanitation

How: To collect materials the romans used mines, mines that used hydraulic mining a process in which water is run into hills revealing the ore and then cutting the rocks around it away and waste debris 

image:NOTE I CANNOT ADD PICTURES FOR SOME REASON SO I'LL JUST EXPLAIN THEM 

Picture: it is of a large (bigger than a person) trebuchet made of wood and duct tape, with a rope attached which when pulled release's the handle on the trebuchets projectile firing it.

to start, back in the 4th century they wouldnt have used duct tape and wood as tape wasnt invented and they used metal and iron bolted and screwed together instead of wood as it was more sturdy/reliable and had a higher endurance letting it last years and years. a rope may have been used to make the trebuchet fire however they more likely used a crank/wind up device. 

Bibliography:

1. https://en.wikipedia.org/wiki/Roman_technology

2. https://en.wikipedia.org/wiki/Ancient_Greek_technology 

3.  (where i got the pictures from)