As I explained in my sermon on Col. 4:5-6, the New Testament, for the most part, treats evangelism as a natural byproduct of the church's faithful witness to the gospel in its manner of life together. Paul's assumption is that people will notice the way we live in community together and demand to know why. So when it comes time to give an answer and proclaim the good news, we need to make sure we understand the best way to do that.
Our English word "gospel" comes from the Greek word euangelion, which comes into English as "evangel". Ev-angel simply means "good news/message". The New Testament words used to describe the preaching of the gospel were used in Greco-Roman culture for the sort of announcements that the emperor would send out all over the empire in order to announce facts that were considered to be good news: the empire had won a major victory over its enemies; a new heir to the throne had been born; etc. People in the first century were accustomed to having heralds come out proclaiming the gospel—the good news—that Caesar was Lord. Needless to say, the Apostles created quite a stir when they went about proclaiming that Jesus was Lord of Lords and king of kings. The most basic summary of the gospel is: "Jesus Christ is Lord."
The preaching of the apostles in the book of Acts gives us a pattern for evangelism and witness. The major focus of the Apostles' was to proclaim the fact that Jesus is Lord and King over all peoples and nations. They proclaimed the historical events of God's saving work (incarnation, crucifixion, resurrection, ascension, etc.) as public truth, not merely personal beliefs. The disciples proclaimed the message that Jesus was the promised Messiah and the world's new king, and they called on people to submit to his reign (for example, Acts 2:36-40 and Acts 17:30-31).
The good news of the gospel is that Jesus has accomplished our salvation, he has conquered death, he has defeated Satan, he has delivered us from the old, fleshly way of life, and he is slowly but surely setting the world right. May God give us grace to live out the resurrection life of Christ together and speak words of life.