1 Corinthians 10:1-14 (NASB)
1 "For I do not want you to be unaware, brethren, that our fathers were all under the cloud and all passed through the sea;
2 and all were baptized into Moses in the cloud and in the sea;
3 and all ate the same spiritual food;
4 and all drank the same spiritual drink, for they were drinking from a spiritual rock which followed them; and the rock was Christ.
5 Nevertheless, with most of them God was not well-pleased; for they were laid low in the wilderness.
6 Now these things happened as examples for us, so that we would not crave evil things as they also craved.
7 Do not be idolaters, as some of them were; as it is written, "THE PEOPLE SAT DOWN TO EAT AND DRINK, AND STOOD UP TO PLAY."
8 Nor let us act immorally, as some of them did, and twenty-three thousand fell in one day.
9 Nor let us try the Lord, as some of them did, and were destroyed by the serpents.
10 Nor grumble, as some of them did, and were destroyed by the destroyer.
11 Now these things happened to them as an example, and they were written for our instruction, upon whom the ends of the ages have come.
12 Therefore let him who thinks he stands take heed that he does not fall.
13 No temptation has overtaken you but such as is common to man; and God is faithful, who will not allow you to be tempted beyond what you are able, but with the temptation will provide the way of escape also, so that you will be able to endure it.
14 Therefore, my beloved, flee from idolatry."
Notice that both verse 6 and 11 tell us the purpose of the Old Testament for Christians. The Old Testament serves as an example, or illustration of what sin is, and how God is going to deal with it.
4 "For whatever was written in earlier times was written for our instruction, so that through perseverance and the encouragement of the Scriptures we might have hope."
This verse also tells us that the Old Testament (i.e. "whatever was written in earlier times") was written for our (Christian's) instructions that we might have hope.
7 "What shall we say then? Is the Law sin? May it never be! On the contrary, I would not have come to know sin except through the Law; for I would not have known about coveting if the Law had not said, "YOU SHALL NOT COVET."
This passage explains to us that the Old Testament (i.e. "Law" here) reveals to Christians what sin is. In a very real way the Old Testament helps us to see clearly what sin is and how God will deal with it.
23 "But before faith came, we were kept in custody under the law, being shut up to the faith which was later to be revealed.
24 Therefore the Law has become our tutor to lead us to Christ, so that we may be justified by faith.
25 But now that faith has come, we are no longer under a tutor.
26 For you are all sons of God through faith in Christ Jesus.
27 For all of you who were baptized into Christ have clothed yourselves with Christ."
Here we see that the purpose of the Old Testament was to lead us to Christ that we might be justified by Faith.
15 "For this reason He is the mediator of a new covenant, so that, since a death has taken place for the redemption of the transgressions that were committed under the first covenant, those who have been called may receive the promise of the eternal inheritance.
16 For where a covenant is, there must of necessity be the death of the one who made it.
17 For a covenant is valid only when men are dead, for it is never in force while the one who made it lives."
Christ is the mediator of the New Covenant, the Old Covenant (Old Testament) is no longer in effect. It is the New Testament that the Christian must follow today.