Quote by morphism
Do you have any specific questions? For general reading material, you could try googling "factoring polynomials over finite fields".

I seem to have figured out how to factor mod p (in a prime field) between a couple documents:
www.science.unitn.it/~degraaf/compalg/polfact.pdf
http://www.math.uiuc.edu/~rash/Ant/AntChapter4.pdf
However, I'm still wondering what other types of finite fields it would be useful to factor over (am I correct in assuming that not all finite fields are prime fields?)