You can start with these notes by Vistoli, which talk about that stuff in the direction of doing stacks and descent theory. The other articles in FGA explained might be useful, as they do a lot of moduli space construction (ie, prove that a given functor is representable). Another place to look would be in Eisenbud and Harris's "Geometry of Schemes" where they characterize schemes among sheaves on CommRing, towards the end of the book.