"They preached the good news in that city and won a large number of disciples. Then they returned to Lystra, Iconium and Antioch, strengthening the disciples and encouraging them to remain true to the faith. 'We must go through many hardships to enter the kingdom of God,' they said." NIV translation
So, even though it appeared that Paul and Barnabas were running from the other cities, they boldly preached the gospel in Derbe and many were saved. Then, they returned to the cities that they had fled. Though it may have seemed that they were running in defeat earlier in the chapter, we now see that they did not surrender the cities to Satan. We also see that they expected hardships in service to God. It seems that many of us today have lost that expectation even though Jesus called us to take up our cross and follow him. Jesus didn't say it would be easy to follow him!
"Paul and Barnabas appointed elders for them in each church and, with prayer and fasting, committed them to the Lord, in whom they had put their trust." NIV translation
Paul and Barnabas realized that there had to be leaders (elders) in the groups of believers (churches) that had been started in the cities.
They could not be everywhere at once and the new believers needed someone to mentor them and help them to grow in their relationship with Jesus Christ.
We see here that they appointed these leaders and through prayer and fasting committed them to the Lord.
"After going through Pisidia, they came into Pamphylia, and when they had preached the word in Perga, they went down to Attalia. From Attalia they sailed back to Antioch, where they had been committed to the grace of God for the work they had now completed." NIV translation
Paul and Barnabas continued their journey of sharing the gospel and then sailed back to Antioch which was their "home church". This was the group of believers that had committed them to God for service.
"On arriving there, they gathered the church together and reported all that God had done through them and how he had opened the door of faith to the Gentiles. And they stayed there a long time with the disciples." NIV translation
When they returned home, they told the people of what God had done through them on their trip. Then, they stayed there "a long time" and built up the local believers. Paul and Barnabas had a great testimony to share with the people as they had saw the hand of God at work in several places. By telling them about it, they could build up the local believers and help them to see that God is bigger than just their little group. This pattern of evangelism was good enough for the most famous "missionary" ever yet, today, most Christians do not pay any attention to how Paul went about it. The pattern today of "relationship evangelism" is not what the early church did. They simply went and stated the good news of Jesus Christ and trusted God to use his word. Today, much money is spent supporting "missionaries" that move to an area to live and share the gospel as if they were some sort of "super Christians".