Allan Moseley poses seven questions that can help us to see how the Old Testament points to Jesus.

1. Is the passage referred to in the New Testament?  For example, Habakkuk 2:3 is directly quoted in Romans 1:17; Galatians 3:11 and Hebrews 10:38.  Sometimes, however, the allusion is not so straightforward, as when, according to Matthew 2:23, it had been written ‘the prophets’ that Jesus would be called ‘a Nazarene’.
2. Does the OT passage address a theme that is also addressed in the NT?  For example, the OT has a great deal to say about the sacrificial system.  A number of passages in the NT (not least Hebrews 9-10) take up this theme and offer commentary on it.
3. Does the passage reveal something about the human problem?  From Genesis 3 onwards, the problem of sin and alienation from God underlies everything that we learn about human character, relationships, and so on.  When we identify any particular manifestation of this, we are led to speak of how in Christ God meets our need.
4. Where is the passage located in salvation history?  We need not only to locate an OT passage in history, but in salvation history.  There is a trajectory in the OT that moves from eternity past, to creation, to human rebellion, to promise, law, monarchy, and exile.  Then, of course, the NT speaks of the incarnation, earthly life and teaching, death, resurrection, ascension and exaltation of Christ, and to his future return and the establishment of God new heaven and new earth.  It is of great importance to show how any particular Bible passage fits on this line: where it has come from and to what it is pointing.
5. Does the passage raise a question that is answered by Jesus or the NT?  To be sure, Psalm 73 answers its own question about the question of the prosperity of the wicked.  But other questions, such as Job’s “Oh, that I knew where I might find him!” are answered by Jesus: “Who has seen me has seen the Father” (Jn 14:9).
6. Does the passage reveal an attribute or characteristic of God?  What the OT ascribes in an undifferentiated way to God, the NT may clarify as an attribute or characteristic of Christ or of the Holy Spirit.  For example, where Genesis 1:1 says that ‘In the beginning God created…”, Colossians 1:16 says that ‘by [Christ] all things were created.’
7. Does the passage refer to something or someone who is a type of Christ?  Consider the tabernacle: in the OT, the tabernacle represented God’s meeting place with his people (Exodus 25:2; 29:43).  According to John 1:14, ‘the Word became flesh and “tabernacled” among us’.  Similarly, the NT speaks of those who are in Christ as the ‘temple’ in which God meets with them by his Spirit  (1 Cor 3:16–17; 6:19; 2 Cor 6:16).

For all these reasons, Jesus could affirm of the OT scriptures that ‘they bear witness about me’ (John 5:39.

(Based on, and in part quoting verbatim from, this article)