"On hearing this, they were baptized into the name of the Lord Jesus. When Paul placed his hands on them, the Holy Spirit came on them, and they spoke in tongues and prophesied. There were about twelve men in all." NIV translation
The men were baptized and received the Holy Spirit. We notice that, when that happened, God's power was immediately displayed as "they spoke in tongues and prophesied". When you are working and walking in the Spirit, God does amazing things. For some it may be these two examples but for others it may be in some other form. As Paul said in 1 Corinthians 12, there are many ways that the Spirit is displayed but they are all important for building up the body of believers.
"Paul entered the synagogue and spoke boldly there for three months, arguing persuasively about the kingdom of God. But some of them became obstinate; they refused to believe and publicly maligned the Way. So Paul left them. He took the disciples with him and had discussions daily in the lecture hall of Tyrannus." NIV translation
As was the pattern in the ministry, Paul went into the local synagogue and boldly proclaimed the gospel. He did this for three months before the people simply refused to believe.
Paul dusted off his sandals and left the building (just as Jesus had told the disciples to do when He sent them out two by two)!
He and the disciples went to a local school (the lecture hall at Tyrannus) and had daily discussions. God had made this possible as the school took a siesta (break during the heat of the day) that lasted two or three hours. It was during this time that they would gather and have daily discussions about their walk in Christ.
"This went on for two years, so that all the Jews and Greeks who lived in the province of Asia heard the word of the Lord. God did extraordinary miracles through Paul, so that even handkerchiefs and aprons that had touched him were taken to the sick, and their illnesses were cured and the evil spirits left them." NIV translation
God did a real work here as we see that in two years time all of the province heard the Word. The news probably spread pretty fast when people started to be healed by simply taking a handkerchief to them. The handkerchief that it is talking about would have been a rag that Paul wiped the sweat off of his forehead with as he worked. This is the only occasion where God did this through Paul and the evil spirits fled from these sweat rags.