What are the relationship between the Old and the New Testaments?

From the very beginning God had a plan for His creation. In the Old Testament we are told how the universe was created (Genesis's, and we are told how the nation of Israel began. Then we are told of the history of Israel. All through the Old Testament we see Scripture that pertains to a coming Messiah. At the end of the Old Testament the Messiah still has not come, but hope still remains in many of the Jews that God's promise will be fulfilled. Approximately 400 years pass from the time the last book in the Old Testament was written (Malachi) and the story of the birth of Jesus begins in the New Testament.
The New Testament is a continuation of the Old Testament, but with many changes.
The Old Testament people were guided by the "old covenant" or the Law of Moses.
When Jesus finished His earthly ministry He died on the cross of Calvary taking the sins of mankind with Him. He paid the price for our sin (But we have to accept Him as our Savior in order to be forgiven of our sins).
When Jesus died and was resurrected the "new covenant" begin (Jeremiah 31: 31-34; Hebrews 8:7-13) This "new covenant" did away with the ceremonial part of the law, but retained the Law of God that is written in our hearts. We do not "get" salvation by following the letter of the law, or by works, but we "get" salvation by faith in the Son of God, which is Jesus Christ. Actually this is the way anyone received salvation, by believing God. Abraham, we are told believed God and it was accounted as righteousness to him. By faith Abraham believed God (Romans 4:1-4; Hebrews 11:8-12; 17-19 ).
Most of the Jews did not believe Jesus was the Messiah and many of them are still looking for a Messiah to come that was God's promise.
The two, Old Testament and New Testament are one story. The New Testament takes us into the future (Revelation) and is the end of God's book to us.