Peter's inaugural sermon of the church, given at Pentecost, is a classic prototype of how we can effectively bring the gospel to our culture. This message does not have a shelf life. It still relates and resonates with us today.
One of the things that made it effective was that Peter knew his audience. He knew that in the Jerusalem crowd he was addressing, there probably were some of the very people who were responsible, literally, for the crucifixion of Jesus Christ. It had been only a couple of months since the crucifixion, and Peter, being an eyewitness of it, may have even recognized them.
Peter's message was filled with Old Testament Scripture, because his goal was to convince them that Jesus Christ was the long-awaited Messiah of Israel. These people were conversant with Scripture. They were raised studying the Torah—the Scriptures. So he referenced the Old Testament repeatedly, showing that Jesus was the Messiah.
Paul, on the other hand, did not have the same kind of infrastructure in his message as he spoke to the Athenians (see Acts 17). There he was speaking to a secular mindset, probably more like what we are dealing with in our culture today. Paul took a different approach and quoted some of their secular philosophers to build a bridge to his audience.
This reminds us there is not a one-size-fits-all approach to evangelism. Some people share the gospel in a robotic way, saying the same thing to every person. But that is not the way to share your faith. You have to adapt to the person you are speaking to.
Peter adapted to his audience. He took time to understand them. He didn't, however, lower his standards to extend his reach. He found common ground with his listeners for the purpose of bringing them to Christ.