As noted, with the high thinking environment in Athens it was also known as a place of learning and culture while Corinth was a place of travelers and commerce. They were only 50 miles from one another but quite different. Years before this the Romans had destroyed Corinth but due to it's valuable location it would not die and was rebuilt some 100 years later. Corinth worshipped idols and was a city plagued by a lifestyle of sexual promiscuity and immorality. They worshipped Aphrodite, the Goddess of love, who led them to use religion as an excuse for such behaviors.
In Corinth, Paul met Aquila, a Jew, who recently came from Italy with his wife Priscilla, who was of noble family heritage. It is not known if they were believers. All we know is that at that time Aquila was a Jew. They left Italy when Claudius Caesar deported all the Jews from Rome. A biographer of Roman emperors named Suetonius gave insight into why the Jews were forced to leave Rome. He wrote The Life of Claudius which discussed the constant riots in Rome for which the Jews supposedly blamed Chrestus. It is believed "Chrestus" was a name referring to Christ.
Paul liked Aquila and Priscilla and stayed with them a while. The fact that they and Paul were tentmakers gave them things in common.
As always, Paul immediately attended the Synagogue and began teaching the Jews and Gentiles about Christ and the Good News. Once Timothy and Silas arrived from Macedonia, Paul devoted all his time to teaching and preaching the word. He boldly professed Jesus as the Messiah. As was common, the Jews opposed him and insulted him. Paul was continually met with such resistance. In Matthew 10:14, Jesus instructed "if any will not listen to you, shake the dust from your feet and leave that town." Following Jesus' advice, Paul shook the dust from his clothes. He told them they had written their own destiny when he said "you're blood is on your own heads," and he was not guilty for causing what would happen to them. Paul then declared that from then on he would preach to the Gentiles and he left the synagogue.
Fortunately, next door to the synagogue there lived a Gentile man, named Titius Justus, who worshipped God and Paul began preaching there. Also, the synagogue leader named Crispus and all in his household believed in the Lord. Many in Corinth heard Paul and became believers and were baptized.
As in every place Paul preached, there was strong opposition and the same had to be true in Corinth which is what may have prompted Paul's encouragement from the Lord saying,
"Don't be afraid! Speak out! Don't be silent! For I am with you, and no one will attack and harm you, for many people in this city belong to me." So, Paul stayed and continued to preach for another year and a half.
When the Roman, Lucius Junius Gallio Annaeus, became Governor/Proconsul of Achaia and ruler of all southern Greece, some Jews rose up against Paul. They brought Paul before Gallio to be judged. They charged Paul with persuading people to worship God in ways that were contradictory to their law. This was a big deal because if Gallio pronounced any judgement, that judgment would then set a legal precedent.
Once charged, Paul began to defend himself but was cut off by Gallio. Gallio declared there was no serious crime that needed him to be involved and that it was only a matter about words and Jewish rules so he dismissed them. He threw them out of the courtroom and told them to go and judge the matter themselves.
Still in the courtroom, the crowd, made up of Greeks, grabbed the synagogue ruler, Sosthenes who replaced Crispus, and beat him. It was clear the Gentiles in Corinth were tired of the Jews and their distaste of them developed into a spirit of antiSemitism. Being in the courtroom, Gallio saw the beating but paid no attention.
Paul stayed in Corinth for some time then went to Cenchrea. While there, according to Jewish custom, Paul shaved his head to mark the end of a vow. The vow may have been made when he went to Macedonia but more likely when he began his ministry in Corinth. When making his vow he most likely let his hair grow and cutting it would be a sign that the vow had ended.
From there he set sail for Syria along with Aquila and Priscilla, stopping at Ephesus along the way to encourage the church there and reason with the Jews at the synagogue. When Paul was getting ready to leave they asked him to stay longer to which he declined. As he left, he told them he would be back later, God willing. He left Aquila and Pricilla there and went on to Caesarea then on to visit the church in Jerusalem. The journey from Ephesus to Caesarea was about 500 miles. Some say Paul was in a hurry to get back to Jerusalem in time to celebrate the Passover. Following his visit to Jerusalem, Paul went back to Antioch. After Antioch, Paul went back through Galatia and Phrygia to strengthen and encourage all the believers there. This was the end of Paul's second missionary journey. This journey lasted about 3 years and covered about 2700 miles. (1410 by land and 1290 by sea.)
Meanwhile, a Jew named Apollos who knew the Scriptures very well and who was a great speaker had come to Ephesus from Egypt. He had been taught the ways of the Lord and taught others with enthusiasm and accuracy. He had to have been well versed in the Old Testament and we are told he taught well but only knew of John's baptism. This can tell us that he was aware of John the Baptist's baptism representing the cleansing of God by repentance to Him. This may also tell us that he was not aware of the baptism of the Spirit which many had been exposed to in earlier chapters in Acts. This Christian baptism is baptism in Christ's death, burial, and resurrection by the Spirit.
Pricilla and Aquila who were still in Ephesus, heard Apollos preaching, took him aside, and taught him the way of God more deeply. Apollos had been thinking about going to Achaia and was encouraged by the believers in Ephesus to go. They wrote to the believers there and asked them to welcome Apollos. When he arrived, Apollos proved to be of great value to those who had become believers by God's grace. His knowledge had become such that he refuted the Jews with powerful arguments in public debates all the while using the Scriptures to make his points. He preached and explained that Jesus was the Messiah.