Here are some good tips by scholar Richard N. Longenecker on how to view the New Testament use of the Old Testament.
“The question is, however, as to what exactly is meant by fulfilment in the biblical sense. One answer is to assert that fulfilment has to do with direct prediction and explicit verification. Indeed, a primary test of a prophet in OT times was that his predictions could be precisely validated at a later time (Dt. 18:22; cf 1 Sa. 9:6). And this same expectation is carried on in the NT, as witness Jesus’ statement on fulfilment in Matthew 5:17-18 (even the most minute features of the prophetic vision shall be fulfilled) and many of the quotations of Scripture by the evangelists (e.g. Mk. 1:2-3, par.; Mt. 2:5-6; Jn. 12:14-15). It is, in fact, this understanding of fulfilment that Justin Martyr used to excess in his Dialogue with Trypho. It appears also in extreme form in many of the Church Fathers; for example, in Tertullian’s claims that Genesis 49:27 (‘Benjamin is a ravening wolf; in the morning he devours the prey, and in the evening he distributes food’), 1 Samuel 18 (Saul’s pursuit of David, but later repentance), and Isaiah 3:3 (‘I will take away from Judah… even the wise master-builder’) are veiled predictions of Saul of Tarsus, who was from the Judean tribe of Benjamin, and so were fulfilled in Paul’s life and ministry (Adv Marc 5.7.10).
So-called ‘proof from prophecy’ of a direct nature has always been a factor in both a Jewish and a Christian understanding of fulfilment. Sadly, however, some see this as the only factor, and so lay out prophecy-fulfillment relations in a manner approximating mathematical precision. Starting from such basic theological axioms as that there is a God in charge of human affairs and that historical events happen according to his will, they point to a few obvious instances where explicit predictions have been literally fulfilled (as Mi. 5:2, quoted with variation in Mt. 2:5-6) and move on from there to construct an often elaborate and ingenious ‘biblical’ apologetic that is usually more ‘gnostic’ than biblical.”
He goes on to say:
Jewish exegesis of the first century can generally be classified under four headings: literalist, midrashic, pesher and allegorical. Admittedly, such a fourfold classification highlights distinctions of which the early Jewish exegetes themselves may not have always been conscious. In dealing with a system of thought that thinks more holistically, functionally and practically than analytically – one that stresses precedent over logic in defense of its ways – any attempt at classification must necessarily go beyond that system’s explicit statements as to its own principles. Nevertheless, we still maintain, Jewish interpretations of Scripture fall quite naturally into one or other of these four categories.