From what ive heard from Stu, before you can judge you need to effectively be 'tested' to make sure the scores you give each contestant are very similar to the ones the rest of the judges give. This is what he was referring to when he mentioned 'shadow' judging. You'd score each person, and they'd check out your scores to make sure they were ok, but they wouldn't actually count.
The actual act of judging involves holding 2 clickers, 1 for positive points, one for negative. Every string hit (each time the yoyo hits a string) on a unique trick (ie they can't do trapeze 800 times, only the first one would count for 1 point) they get a point. Every time they stuff up, ie miss a trapeze, they loose a point. Changing a yoyo counts for more (-ve points). Thats as much as I know about it. Im not sure what else gets points, ie things like suicides, or other slack tricks (ie yoyo never hits a string, but they do lost of other cool things)