"And beginning with Moses and all the Prophets, he interpreted to them in all the Scriptures the things concerning himself." Luke 24:27
Jesus makes the bold claim that the Old Testament scriptures testify to him. We should understand this statement in the richest and deepest way possible. The Old Testament isn't only tangentially about Jesus. Jesus is the beating heart of the scriptures, their true core and focal point.
Here's a hopefully helpful list of 5 ways we find Christ in the Old Testament. This is not meant to be exhaustive, but gives a framework for seeing Christ as we study the OT.
1) Direct (Rectilnear) Prophecy:
These are the prophecies which we understand speak of the Christ in a way of direct prediction.
Some examples might be Genesis 3, where the Seed of the woman will crush the head of the serpent. Or Isaiah 7, in which a virgin will conceive and bear a son, or Micah 5, "You, O Bethlehem" predicting the place of His birth.
People, events, even animals from the stories of the Old Testament often foreshadow New Testament fulfillments. The flood prefigures Baptism. Sarah and Hagaar typify the two covenants. This is not to say the original stories aren't true, of course. But they also serve as shadows of other things to follow.
Likewise, much of the Old Testament hints at, points to, or even screams about Christ! Take the Passover for one example - in which the people of God are saved by the blood of the lamb. Or the Day of Atonement, in which the sins of the people are placed upon the scapegoat, which is then sent off to die. Or the whole ceremonial and sacrificial system, which in many ways, shows forth a testimony of Christ - who is God With Us in the tent of human flesh.
Some of these are spelled out very clearly by the New Testament. For instance, Jesus tells Nicodemus that the bronze serpent Moses lifted up pointed to him, "the Son of Man must be lifted up, that whoever believes in him might have eternal life." John 3:14-15. Or take "the sign of Jonah", by which Jesus compares his death and resurrection with Jonah's 3 days in the belly of the great fish.
3) The "Golden Thread"
Another very straightforward way to see Christ in the Old Testament is to simply trace his lineage. So the stories of Adam, Seth, Noah, Shem, Abraham, Issac, Jacob, Judah, David and Bathsheba, Solomon, Ruth, and so many others - show how God was bringing about the fulfillment of His messianic promises.
The genealogies of Matthew's and Luke's Gospels are helpful here, as a sort of a road-map for finding the Golden Thread.
A theophany is a visible manifestation of God. The Old Testament contains many of these, and I would argue that when they happen, we do better to assume they are the Second Person of the Trinity than automatically thinking it's God the Father. So for instance, at the burning bush, it was God the Son who spoke to Moses. God the Son who walked in the garden of Eden and called, "Adam, where are you?". God the Son who appeared to Abraham along with the two angels. God the Son who manifested as pillar of cloud and pillar of fire. God the Son who is seated between the cherubim on the Mercy Seat of the Ark.
The various appearances of the Angel of the Lord also seem to be a pre-incarnate manifestation of the Second Person of the Trinity.
5) Christ IS the Word
Finally, and perhaps most profoundly, Christ IS the very living Word of God (John 1). So every word of Scripture not only testifies to him, but in a way we can't fully grasp - the word is God.. the Son.
For further study: