In examining Peter's sermon in Acts 2 and then Paul's sermon in Acts 17, we see the starting point for each sermon was entirely different. In Acts 2, Peter begins by quoting the prophet, Joel, and says that "everyone who calls on the name of the Lord will be saved" (Acts 2:21). He then moves right into telling them about Jesus, whom they knew.
In Acts 17, Paul had to adapt the start of his sermon because he was speaking to a group of people who were worshipping many different gods. In fact, it is estimated that there may have been about 20,000 different gods. There was one altar that had the inscription "TO AN UNKNOWN GOD" (Acts 17:23) and that is where he starts--God, the Creator, the Lord of heaven and earth.
Lord, give us wisdom to know where people are spiritually in our sphere of influence and give us the wisdom to know how to share the gospel with them.