Acts 17 provides us one picture of how Paul evangelized the lost. In the city of Athens, we learn he went to the synagogue to engage the Jews on the Sabbath, and the rest of the week he went to the marketplace to engage the more secular minded in the city.
The marketplace was a huge open-air area in the middle of town where everyone gathered for business, arts, buying and selling, or just to hang out with their friends. We don't really have anything like it today. Technology has allowed us to spread out and do all these things from the comfort of our office or home. However, in Paul's day, the marketplace was where everything happened. It was where everyone gathered.
I would imagine Paul walking around the Market Place, getting to know folks, and then engaging small groups here and there with the gospel.
Today we should do the same. We should reach out, build relationships with folks, and engage them with the gospel where they are on a daily basis. Our marketplace might look different than Paul's. Instead of everything huddled into one area, it's spread out. We work in one part of town, shop in another, eat and drink our coffee someone else.
Even though our marketplace looks different than Paul's, I believe the principle still applies. We should do what Paul did reach out, build relationships with folks, and then engage them with the gospel where they are on a daily basis.