Before the coming of Jesus, John preached repentance and baptism to all the people of Israel. 25 As John was completing his work, he said: ‘Who do you suppose I am? I am not the one you are looking for. But there is one coming after me whose sandals I am not worthy to untie.’26 “Fellow children of Abraham and you God-fearing Gentiles, it is to us that this message of salvation has been sent. 27 The people of Jerusalem and their rulers did not recognize Jesus, yet in condemning him they fulfilled the words of the prophets that are read every Sabbath. 28 Though they found no proper ground for a death sentence, they asked Pilate to have him executed. 29 When they had carried out all that was written about him, they took him down from the cross and laid him in a tomb. 30 But God raised him from the dead, 31 and for many days he was seen by those who had traveled with him from Galilee to Jerusalem. They are now his witnesses to our people.32 We tell you the good news: What God promised our ancestors 33 he has fulfilled for us, their children, by raising up Jesus. As it is written in the second Psalm: “‘You are my son today I have become your father.’34 God raised him from the dead so that he will never be subject to decay. As God has said, “‘I will give you the holy and sure blessings promised to David.’35 So it is also stated elsewhere: “‘You will not let your holy one see decay.’36 “Now when David had served God’s purpose in his own generation, he fell asleep; he was buried with his ancestors and his body decayed. 37 But the one whom God raised from the dead did not see decay.38 Therefore, my friends, I want you to know that through Jesus the forgiveness of sins is proclaimed to you. 39 Through him everyone who believes is set free from every sin, a justification you were not able to obtain under the law of Moses."
Paul's message continues. He had already established that God created man and chose the Israelites to be in a relationship with Him but because of their trespasses they couldn't be and were receiving, even right then in their oppression by the Romans, the punishment for their sins. He then goes on to tell them that John the Baptist told them that they needed to repent and show it by humbling themselves to wash in symbolic water of becoming a new Jew the way the Gentiles had to if they wanted to convert. Then he introduces Jesus, from the lineage of David whom John the Baptist introduced as greater than him because He could actually remove sins because as God, the sins were done against Him. Jesus did this by dying on the cross. He took away the sin of the world, as John the Baptist said He would by taking on the curse we deserved because "cursed is everyone who dies on a tree" and the death we deserved because "the soul that sins must die." He shed His blood for us because "without the shedding of blood there is no forgiveness of sin." He was the ceremonial scapegoat if we by faith put our sins on Him, He would take them "out of the camp." Then He rose from the dead as Isaiah said, "After He suffered He would see the light of life and God would prolong His days." Because of this when we die we too can live on by trusting in Him.
This is the whole gospel to Jews as spelled out in the Old Testament. He spoke to them in their language. Using the New Testament we have
"for all have sinned and fall short of the glory of God, 24 and all are justified freely by his grace through the redemption that came by Christ Jesus. 25 God presented Christ as a sacrifice of atonement, through the shedding of his blood—to be received by faith. Rom. 3:23-25
24 “He himself bore our sins” in his body on the cross, so that we might die to sins and live for righteousness; “by his wounds you have been healed.” 1Peter 2:24
If you declare with your mouth, “Jesus is Lord,” and believe in your heart that God raised him from the dead, you will be saved. 10 For it is with your heart that you believe and are justified, and it is with your mouth that you profess your faith and are saved. Rom.10:9,10
God made him who had no sin to be sin for us, so that in him we might become the righteousness of God. 2Cor. 5:21
For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life. John 3:16
Do you have these verses memorized or some others that at a moment's notice you can share and lead someone to Christ? Paul did and he had some for every distinct audience. We need to also.