I have sometimes hard time reading papers that are written in the language of schemes being replaced by the functors they represent (I have especially homotopy scheme theory in mind). 


I think the topic is connected to topoi and Grothendieck topologies, but for now I'm looking for something simple, just the working overview of the language of representable functors, what is a scheme, etc.



"Every scheme as a sheaf" references?
You can start with [these](http://homepage.sns.it/vistoli/descent.pdf) 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.


