There are two basic forms of homiletics. They are evangelistic (preaching the gospel to those who are not Christians) and pastoral (teaching those who have the Spirit of God in them).
Evangelistic Homiletics
An example of evangelistic preaching is the message the apostle Paul spoke on Mars Hill to pagan god worshipping Athenians.
Then Paul stood in the center of Mars' hill and said, "Men, Athenians, I perceive that in all things you are very reverent to deities;
"For as I was passing through and observing the objects of your veneration, I also found an altar on which was inscribed, 'To an unknown God.' So then, He Whom you worship in ignorance is the One that I proclaim to you." (Acts 17:22 - 23, HBFV).
Pastoral Homiletics
Examples of pastoral homiletics are Christ's discourses to his disciples during and after his last Passover (John 13 - 16) and the apostle Paul's all-day teaching to the disciples at Troas.
Now on the first day of the weeks, when the disciples had assembled to break bread, Paul preached to them; and because he was going to leave in the morning, he continued speaking until midnight. (Acts 20:7, HBFV).
The apostle Paul was one of, if not the, most effective teacher and preacher in the New Testament. While he personally shunned messages in the style of those who wished to deceive or please others (1Thessalonians 2:2 - 3, 5), he adapted what and how he spoke (his homiletics) based on his audience.
Paul's Appeals
To the pagans in Athens Paul appealed to their pursuit of knowledge in order to reveal the REAL God (Acts 17:22 - 31). To Jews he spoke from a Jewish point of view.
For although I am not under bondage to anyone, I have made myself a servant to all, so that I might gain the more.
Now to the Jews I became as a Jew, that I might gain the Jews; to those who are under law, as under law, that I might gain those who are under law (1Corinthians 9:19 - 20, HBFV).
He encouraged his friend, the young evangelist Timothy, to give himself fully to those things that would make his preaching effective (1Timothy 4:12 - 15).
Augustine of Hippo (354 - 430 A.D.), a bishop in the Catholic Church, is thought to be the first person to record basic principles and rules for homiletics in his work "On Christian Doctrine."