Acts 16 :6-15
Paul and Silas and, and I assume Timothy, continued on their missionary journey. At this point, because the language of the text changes from third person to first person plural, we can assume Luke, the author, has joined them too.
This small group traveled to more towns where assemblies (churches) were established. Paul had planned to go on in the same direction, but the Holy Spirit stopped them. Probably it was in prayer that they heard the change in plans.
Then Paul had an encounter with the Holy Spirit and in a dream he heard a man calling for help in another region. Paul was used to being directed by by the Spirit so they changed their plans and went to the region of Macedonia.
Instead of going east they went west towards Greece. What transportation was there to do this? They could continue on foot for a long time around the coast or find someone with a boat to take them over to the other coast. Troas was right on the great sea (the Mediterranean) and would give them an opportunity to find a merchant who was sailing to Greece.
We know it takes money to go on a ship but there are few clues as to where they got their money. We know from other books that Paul would spend time as a tent maker and that he received donations from some of the assemblies he had started.
They sailed to Philippi then went by foot again. While there, they went looking for other Jews on the Sabbath. They went to the riverside to look for a gathering, which was usual for Jews in a gentile city with no established synagogue. they found some women there. A Synagogue had to have 10 men but these women were wanting to worship anyway.
This city was settled by Romans as a cultural toehold to influence the people in the area. So the city was mostly Roman instead of Greek. The Romans were considered worse than the Greeks because they desecrated the temple. So Paul was seeking to convert enemies to Christ.
There were some gentile followers of God with the Jews who listened to Paul and wanted more information. Paul probably spoke on how Jesus of Nazareth fulfilled the prophecies of the Messiah as well as news of how Jesus healed people and cast out demons.
Among them was a woman of business (dealt in purple, a very expensive dyed fabric) who believed him; her name was Lydia. She was so taken with the news of the kingdom and Jesus as Messiah she wanted to be baptized as an affirmation of her belief. Her whole family and household was baptized, this probably included children and slaves.
Since she was a woman of business, she probably had a comfortable home. So she honored them, asking Paul and his companions to come stay at her house. This convert was important in the work of teaching about the faith. We are not told how long they were there, only that it was some days not weeks. This was the seed of a new assembly or church.
This is one incident of a woman being in charge of believers. Lydia could hold worship at her house. She was enthusiastic about Jesus and sharing her testimony was a way of leading. Since she already had a business she was obviously able to lead others. She could be trusted to take care of people too. This is a case of woman being together with men in service. In Gods eyes whoever was available was to serve.