MS08-067 As used by Conficker and Stuxnet

How do Worms travel?

Strictly speaking, a computer virus doesn't spread across a network whereas a computer worm can travel from machine to machine. But how do worms move between machines?

A vulnerability with the catchy name of MS08-067 was used by Stuxnet and Conficker to worm themselves across Local Area Networks but how did it work?  I spent a reasonable amount of time reverse engineering the vulnerability to discover how it was exploited.