JWBN: I'm having exactly the same problem. I sent the workers to school, but that didn't help. Am stuck! :(
There are different kinds of workers for different resources. Transporters ONLY move supplies around, they don't actually harvest it (except food from bushes). Stonecutters ONLY harvest stone, they don't build buildings or chop wood.
If you've got stonecutters standing around doing nothing, then you should be able to control them like in most other RTS (left click to select them, right click on a stone to tell them to gather it).
If you don't have any stonecutters, then yeah, the school is the way to get them. You select the school, then go to the production tab where you train other units. The stonecutter is unlocked by default (I think) but he's not on the first page, you need to scroll down with those blobby red triangles at the bottom of the box (or the mousewheel) to see him. The only resource you need to train one is gold (and someone to train).
edit: Ugh, mixed up stonecutters and lumberjacks originally. Lumberjacks are trained the same way as stonecutters, bascially, except I don't think you need to scroll to get to them on the school screen but they need to be researched first from the lab.