Can someone please recommend books that deal with the techniques used to apply General Relativity at Global scales? Einstein's Field Equations are local statements, so is there a technique or a whole book that deals with how to get global information using them?
Before answering, please see our policy on resource recommendation questions. Please write substantial answers that detail the style, content, and prerequisites of the book, paper or other resource. Explain the nature of the resource so that readers can decide which one is best suited for them rather than relying on the opinions of others. Answers containing only a reference to a book or paper will be removed!
Global methods in GR were used by Roger Penrose in the sixties to establish the singularity theorem of black holes, and are a combination of topological techniques. These methods were further expanded by Hawking and Penrose to prove that the big bang is a space-time singularity, and further employed by Hawking to establish the properties of the absolute horizons of black holes.
Rather understandably, the book by Hawking and Ellis, which was written in 1973, draws much material from Hawking's pioneering work on the topic, while Wald's book is a self-contained, slightly more modern introduction to much of the same material and techniques.
Since then, global methods have become a major topic of research, at the frontier between mathematics and physics. Depending on your level of sophistication you may read either a chapter like Causal structure and global geometry in Wikipedia, or some rather nice lecture notes given at Columbia. Just remember to brush up on your understanding of Raychaudhuri's equation ;-)