How are we to live in today's secular culture? In the book of Acts, what was Paul's approach to the pagan people of Greece?

Most of the people of Athens were well educated, but they were also pagan, and worshipped many Greek gods.

Paul's approach to his sermon to the people of Athens was very consistent with what he taught about going out into the world and dealing with a secular pagan culture—how to deal with those outside of the faith.

Paul did not argue or try to convince people. He reasoned with them, starting with what they already knew. 

Acts 17:16-20 "While Paul was waiting for them in Athens, he was greatly distressed to see that the city was full of idols. So he reasoned in the synagogue with both Jews and God-fearing Greeks, as well as in the marketplace day by day with those who happened to be there. A group of Epicurean and Stoic philosophers began to debate with him. Some of them asked, “What is this babbler trying to say?” Others remarked, “He seems to be advocating foreign gods.”

They said this because Paul was preaching the good news about Jesus and the resurrection. Then they took him and brought him to a meeting of the Areopagus, where they said to him, “May we know what this new teaching is that you are presenting? You are bringing some strange ideas to our ears, and we would like to know what they mean.”