Now some collected links from around the web:
From University of Victoria: http://www.math.uvic.ca/faculty/gmacgill/guide/GenFuncs.pdf
The textbook from MIT's Mathematics for Computer Science
Just go down to the Generating Functions chapter and click to it.
The Guru of generating functions himself: http://www.math.upenn.edu/~wilf/DownldGF.html
Let's solve a recurrence relation with a generating function solution.