See Illusie.
http://ncatlab.org/nlab/show/cotangent+complex
http://mathoverflow.net/questions/2607/intuition-about-the-cotangent-complex
Groth in LNM0079 on relative cot complex and additive cofibred cats
An excellent introduction to derived AG is the CRM 2008 notes, in Toen web unpublished folder. These notes also covers algebraic stacks, the idea of moduli spaces, a little about cotangent complexes, and examples of derived algebraic stacks.
arXiv:1008.0601 A note on the cotangent complex in derived algebraic geometry from arXiv Front: math.AT by Gabriele Vezzosi This note is supposed to answer some questions on deformation theory in derived algebraic geometry. We show that derived algebraic geometry allows for a geometrical interpretation of the full cotangent complex and gives a natural setting for deformation and obstruction theories.
nLab page on Cotangent complex