How did they read the Old Testament: literally, or as types and figures of Christ?

Letter of BarnabasLetter of Barnabas 7.3–5

He himself was going to offer the vessel of the Spirit as a sacrifice for our sins, so that the type that took place in Isaac, who was offered on the altar, might be fulfilled. What then does he say in the prophet? "And let them eat of the goat that is offered at the fast for all their sins." Pay close attention.

An early, bold reader of types. Barnabas finds Christ in the Day of Atonement ritual and in Isaac. He also says the Jewish food laws were always meant spiritually, which later writers did not follow.

Justin Martyr c. 100–c. 165 ADDialogue with Trypho 90.4–5; 91.4

Moses himself prayed to God with his hands stretched out on either side, and Hur and Aaron held them up all day, so that he would not grow tired and let them droop. For if he gave up anything of this figure that imitated the cross, as it is written in the writings of Moses, the people were being defeated; but if he remained in this posture, Amalek was being conquered. ... And the setting up of the serpent, through the type and sign, against those who were biting Israel, is shown to have been done for the salvation of those who believed, because through the one who was going to be crucified, death was from then on proclaimed beforehand to the serpent, and salvation to those bitten by it and fleeing for refuge to the one who sent his crucified Son into the world.

Justin has just won Trypho's agreement that the prophets revealed things in parables and types (90.1 to 2). Moses' outstretched hands and the bronze serpent are his worked examples of types of the cross.

Origen of Alexandria c. 185–c. 254 ADOn First Principles 4.2.4

So each person must write the meaning of the divine writings threefold in his soul: the simpler are built up by what we may call the body of Scripture, which is the common, historical sense; those who have begun to advance and can see further, by its soul; and the perfect, of whom the apostle says "we speak wisdom among the perfect" (1 Corinthians 2:6), by the spiritual law itself, which holds a shadow of good things to come. For as a human being is said to be made of body, soul and spirit, so is holy Scripture.

The founding statement of the spiritual sense. Origen also says a few passages cannot be true literally and point beyond themselves (4.3.1). Survives in Rufinus's Latin and in the Greek of the Philocalia.

Augustine of Hippo 354–430 ADOn Christian Teaching 3.10.14

This is the method for telling whether a saying is literal or figurative: whatever in God's word cannot be referred in its proper sense either to good conduct or to the truth of faith, you must know to be figurative. Good conduct is the love of God and neighbor; the truth of faith is knowing God and neighbor.

Augustine also insisted that the historical events really happened; his Literal Commentary on Genesis reads Genesis as history.

Westminster Confession (Reformed)Westminster Confession of Faith 1.9

The infallible rule of interpretation of Scripture is the Scripture itself: and therefore, when there is a question about the true and full sense of any Scripture (which is not manifold, but one), it must be searched and known by other places that speak more clearly.

The Reformers rejected the medieval four senses of Scripture in favor of one sense, which can include types the text itself intends.