Paul and Barnabas are in Antioch when the Holy Spirit sends them off to proselytize. They go to Cyprus, where Paul blinds the magician Bar-Jesus (literally “son of Jesus”) for opposing their message. They then visit Pamphylia and preach to the synagogue in Perga, where Paul summarizes the Israelites’ history from the Exodus to King David and the life and death of Jesus, portraying him as a fulfillment of Old Testament prophecies; many Jews convert, but many others reject his message and contradict him. He therefore proselytized among the Gentiles. Something similar happens in Iconium: he preaches to Jews and Gentiles, the unbelieving Jews try to persecute them, and they flee to Lyaconia. In Lyaconia, Paul heals a paralytic and preaches. Jews go there from Antioch and Iconium and stone Paul, but he survives. Paul and Barnabas return to Antioch (in the Levant), after passing through Lystra, Iconium, Antioch (in modern Turkey), and Perga.
Certain people from Judea come to Antioch, teaching that the uncircumcised cannot be saved. Paul and Barnabas, unhappy with this, are sent to Jerusalem. Peter, Paul, and Barnabas together convince the apostles and elders that circumcision is unnecessary; James decides that Gentiles should “abstain only from things polluted by idols and from fornication and from whatever has been strangled and from blood.” Paul and Barnabas are sent to Antioch, where they decide to revisit the cities where they proselytized. Barnabas wants to take John with them, but Paul refuses; they part ways.
Note: This page shows a map of Paul’s first missionary journey (map 18), which is described in the summary above.
Here, we see an official decision by the Jerusalem church to admit Gentiles into the religion without requiring circumcision. The decision is made by James, the brother of Jesus. However, note that Gentiles still need to follow some dietary restrictions: they cannot eat meat sacrificed to idols, animals that have been strangled, or blood.
Near the end of chapter 16, Paul has a bitter dispute with Barnabas. This dispute became known as the Incident at Antioch. In Acts, the dispute is because Barnabas wanted to take John Mark on the second missionary journey while Paul refused. In Paul’s own letter to the Galatians, he describes the matter differently:
When Peter came to Antioch, I opposed him to his face, because he was clearly in the wrong. Before certain men came from James, he used to eat with the Gentiles. But when they arrived, he began to draw back and separate himself from the Gentiles because he was afraid of those who belonged to the circumcision group. […] The rest of the Jews joined in this charade and even Barnabas was drawn into the hypocrisy. (Gal 2:11-13)
So Paul’s dispute is with Peter, who refuses to eat with the Gentiles. Barnabas sides with Peter, causing him to be at odds with Paul. Notice that according to Paul–and in sharp contrast to Acts–James is highly conservative on the matter of Gentile converts to Christianity. He believes Jewish law (or at least circumcision) should be followed by Gentiles as well, and even sent men to Antioch who reinforced his point of view.