I would highly recommend chapter 3 from Chriss and Ginzburg's textbook "Representation Theory and Complex Geometry" (really, the entire book is worthy of recommendation).
In a very similar vein, I would also recommend Ginzburg's article "Geometric methods in the representation theory of Hecke algebras and quantum groups", which can be found on the arxiv at: http://arxiv.org/abs/math/9802004. In some ways, I actually prefer these notes to the aforementioned textbook.
While I'm not quite as familiar with it, the textbook "Nilpotent orbits, primitive ideals, and characteristic classes" by Borho, Brylinski, and MacPherson is a very nice reference. In my opinion, however, it serves as more of a secondary reference if you're just interested in the basics of the Springer resolution.
This article and two textbooks, together with the abundant references found within, should be more than enough to get you started. There are, of course, numerous papers on the subject. In particular, I would recommend the 1983 paper by Borho and MacPherson.