I want to recommend several books, articles, and chapters that you may find helpful when studying how the NT authors used the OT. I am not saying I agree with every resource below or that I identity with every author mentioned, but these are works that the serious student of NT use of the OT should consider studying:
A. Beale, G. K. and D. A. Carson, eds. Commentary on the New Testament Use of the Old Testament. Grand Rapids: Baker, 2007. This book is a massive and impressive effort comprised of many different scholars. It does not lay out a specific theory or approach for understanding how the NT uses the OT but the information in it is very helpful.
B. Berding, Kenneth and Jonathan Lunde, eds. Three Views on the New Testament Use of the Old Testament. Grand Rapids: Zondervan, 2008. This book contains entries from Walter Kaiser, Darrell Bock and Peter Enns. They also interact with each other’s chapters. I highly recommend this book.
C. Dean, Rynold D. Evangelical Hermeneutics and the New Testament Use of the Old Testament. Iron River, WI: Veritypath Publications, 2009. A good survey of the major views of NT use of the OT. Much attention is given to Robert Thomas’s Inspired Sensus Plenior Application approach.
ARTICLES / CHAPTERS
A. Bock, Darrell L. “Part 1: Evangelicals and the Use of the Old Testament in the New.” Bibliotheca Sacra 142/567 (July 1985): 209–220. Parts 1 and 2 lay out four major approaches to NT use of the OT. Bock was one of the first to lay out the different major approaches and how they differ with each other. This work is 25 years old now but a must read for serious students of this issue.
B. Bock, Darrell L. “Part 2: Evangelicals and the Use of the Old Testament in the New.” Bibliotheca Sacra 142/567 (October 1985): 306–16. See comments above.
C. Dyer, Charles H. “Biblical Meaning of Fulfillment,” in Issues in Dispensationalism, eds. Wesley R. Willis and John R. Master. Chicago: Moody Press, 1994, 51–72. This is a very helpful discussion of what Matthew means by the term “fulfill” (pleroo).
D. Moo, Douglas. “The Problem of Sensus Plenior,” in Hermeneutics, Authority, and Canon. Eds. D. A. Carson and John D. Woodbridge. Grand Rapids: Zondervan, 1986, 179–211. Helpful discussion of key historical and hermeneutical issues.
E. Nicole, Roger. “New Testament Use of the Old Testament.” http://www.bible-researcher.com/nicole.html This article helps with understanding the various ways the NT writers used the OT.
F. Thomas, Robert L. “The New Testament Use of the Old Testament,” in Evangelical Hermeneutics: The New Versus the Old. Grand Rapids: Kregel, 2002. Thomas argues for Inspired Sensus Plenior Application.
G. Walton, John H. “Inspired Subjectivity and Hermeneutical Objectivity,” The Master’s Seminary Journal 13/1 (Spring 2002): 65–78. Walton argues that the inspired NT authors sometimes used the OT subjectively while he still affirms the objective meaning of OT texts.