Douglas Ulmer recommends: "For an introduction to schemes from many points of view, in particular that of number theory, the best reference by far is a long typescript by Mumford and Lang which was meant to be a successor to “The Red Book” (Springer Lecture Notes 1358) but which was never finished. These notes have excellent discussions of arithmetic schemes, Galois theory of schemes, the various flavors of Frobenius, flatness, various issues of inseparability and imperfection, as well as a very down to earth introduction to coherent cohomology. Some of this material was adapted by Eisenbud and Harris, including a nice discussion of the functor of points and moduli, but there is much more in the Mumford-Lang notes." Unfortunately I saw no scan on the web.
A preliminary, highly recommended version is online here.