What biological processes cause leaves to change colours in Autumn?
Here is a quite nice Chemistry of Autumn Leaf Color. And here is a less chemical, but more detailed explanation regarding the triggering of colour change, which is quite similar to the one from the University of Illinois that @Oreotrephes already gave.

As I understand it, during sunny days a lot of chlorophyll is broken down, but also built up. When after the summer the days get cold and dark, chlorophyll is built up slower (or not any more at some point) and you start to see the colour from the carotenoids and anthocyanins. A harsh change from sunny to cold and dark is supposedly bringing up the brightest colours. At some point, also the carotenoids break down and leaves get brown. The faster the change to cold and dark the larger is the frame between having all chlorophyll broken down and having the other colouring molecules broken down (-> bright colours).

But that's the amateurs explanation.