In his latest post, Larry Hurtado encourages New Testament scholars to more seriously engage the Septuagint when trying to explain OT allusions or citations of the NT. Here is a little provocation intended to move you quickly toward reading the whole thing:
The first/primary question about any OT text thought to have been used in the NT is what the Greek form of the text was. Indeed, at the risk of being provocative, I would say that you need to justify consulting or at least making much of the Hebrew text.
Should you find yourself convicted of neglect and eager to repent, he points to a few helpful introductory resources. I have also posted reviews of three introductions to the Septuagint--including Jobes and Silva, which he mentions--on the book reviews page.
Though Jennifer Dines' introduction is shorter, Jobes and Silva is certainly the place to start. One way of framing the difference between those two reader friendly introductions: Dines answers the question "What is the Septuagint?" Jobes and Silva answer that question plus "What is Septuagint studies?"
Larry Hurtado posted a follow-up, noting another helpful resource, Hengel's The Septuagint as Christian Scripture.
John Meade over at the Evangelical Textual Criticism blog noted Hurado's original post. Be sure to check out John's post because he links to a PDF of the Cambridge (Brooke-McLean) LXX! If you click the link to download it, note that the third "PDF" link on the left side of the archive.org page combines all eight volumes into one.