"After spending some time in Antioch, Paul set out from there and traveled from place to place throughout the region of Galatia and Phrygia, strengthening all the disciples." (Acts 18:23)
And so Paul began the third of his missionary journeys. See also Paul's First Missionary Journey and Paul's Second Missionary Journey.
The first stage of the journey was overland in Asia Minor, through the cities of the regions of Galatia and Phrygia, including Tarsus and Iconium. He eventually reached Ephesus, where he remained for nearly three years (Acts 19:1-41). The apostle John would later include Ephesus as one of the seven cities in the list of churches given in Revelation chapters 2 and 3.
Paul did tremendous work in Ephesus, preaching and teaching the Gospel of Jesus Christ. God permitted many miracles to be done through him, including the healing of the sick and casting out of Demons (Acts 19:11-12). Even Sorcerers turned from their evil practices and repented upon witnessing the power of God (Acts 19:17-20).
As was so often the case, Paul eventually found himself in grave danger from idol worshipers, in this case that of the pagan god Artemis (also known as "Diana of the Ephesians"), and those who were in the business of supplying them (Acts 19:24-27). He exposed their fraud, and in return they nearly killed him (Acts 19:28-41).
Paul then left for Macedonia, and after traveling through the area, arrived in Greece, where he remained for three months (Acts 20:1-3). Very shortly before his departure from Ephesus, Paul wrote his First Epistle to the Corinthians.
While awaiting to sail for Syria, Paul discovered another plot against him, so he instead returned through Macedonia (Acts 20:3). Upon reaching Philippi, and after observing the Feast of Unleavened Bread there, he sailed across to Troas (Acts 20:6).
From Troas, Paul made his way through Assos, Mitylene, Kios, Samos and Miletus (Acts 20:13-16). It was at Miletus that the church elders from Ephesus came up to meet with him for the last time (Acts 20:17-38).
Paul then made the final stage of the voyage, by way of Cos, Rhodes, Patara, Cyprus, and then over to Syria where he landed at Tyre. From there he made his way through Ptolemais, Caesarea, and finally up to Jerusalem.