Paul leaves Athens and goes to Corinth, where he meets a couple of Italian Jewish tentmakers who have been exiled by the Roman emperor, Claudius. Their names are Aquila and Priscilla. He stays with them and makes tents, because apparently that was his trade before he became a zealot. On sabbath days, he hectors people in the synagogue. Eventually they get tired of him, at which point he shook his raiment (v. 6), which I guess is some kind of insult, and declares he's done and he's going off to harangue the Gentiles. The Jews tell him not to let the door hit him in the ass on his way out.
He soon finds himself in the home of a man with the improbably perfect rap name of Justus, whose house abuts the synagogue. He also manages to convert the chief priest, Crispus, and several other members. So much for distancing himself.
One night, god comes to Paul in a dream and tells him to keep up the good proselytising, and not to worry, because he's moved plenty of eager converts into this city. All goes well for the next 18 months, until some dude named Gallio takes over as governor, at which point the Jews arrest Paul and take him to court. But Gallio just sort of scoffs and tells them to come back when there's a serious crime taking place, and to deal with it themselves. The Greeks take Sosthenes, now the chief ruler of the synagogue, and beat him, which does not please Gallio.
Paul stays for another few months, then goes to Syria with Aquila and Priscilla. He also shaves his head, because he's taken some sort of vow. The commentaries are really vague, so I'm not going to think too hard, either. Then he goes to Ephesus to harangue people in the synagogue. Amazingly, they want him to stay, but he refuses, because there's a feast in Jerusalem that he doesn't want to miss.
In his absence, someone named Apollos shows up and starts preaching, but he isn't very well-versed in the scripture, so Aquila and Priscilla try to give him some lessons. After awhile, he decides to leave as well to go and argue with the Jews in a new place.