Read the excellent proof of Yoneda's lemma in wikipedia.
Read the short section on "functor of points" in Mumford's "Lectures on curves on an algebraic surface. For reviewing the basics of schemes etc., Mumford's Red book will be useful.
I think this is the simplest and most compact way of getting started. Then one can move on with the sources suggested by other people in other answers to this question.
I hope my answer is not "too introductory".