How did they answer pagans and Jews?

Justin Martyr c. 100–c. 165 ADFirst Apology 30

So that no one may answer us: "What prevents the one you call Christ, a man born of men, from having done what we call his mighty works by magic, and so seeming to be the Son of God?", we will now give our proof, not trusting those who merely assert, but necessarily persuaded by those who prophesied before the events, since we see with our own eyes things happening and having happened as they were foretold. This, we think, will seem to you too the greatest and truest proof.

Fulfilled prophecy was the main argument to pagans, followed by the moral change in converts.

Justin Martyr c. 100–c. 165 ADSecond Apology 13.4

Whatever has been well said among all people belongs to us Christians. For next to God we worship and love the Word, who is from the unbegotten and inexpressible God, since for our sake he became man, so that, sharing our sufferings, he might also bring healing.

To pagans: Christianity as the true philosophy, the full Word of which philosophers had seeds.

Justin Martyr c. 100–c. 165 ADDialogue with Trypho 11.1–2

There will never be another God, Trypho, nor has there been from eternity, I said to him, but the one who made and ordered this universe. We do not think there is one God for us and another for you, but the very one who brought your fathers out of the land of Egypt with a mighty hand and an outstretched arm. ... But I have read, Trypho, that there would be a final law and a covenant.

To Jews, the argument was over the reading of the same Scriptures. Justin's tone with Trypho is courteous; some later writers against the Jews were harsh.

Tertullian c. 155–c. 220 ADAgainst the Jews 1

Yet we have God himself as a fit promiser and a faithful guarantor, who promised Abraham that in his seed all the nations of the earth would be blessed, and that from the womb of Rebecca two peoples and two nations would come forth.

Written after a public debate with a Jewish proselyte, the treatise argues from the shared Scriptures that the nations were always meant to be admitted to God. Its second half, from chapter 8, reuses material also found in Against Marcion; this opening argument is its own.

Origen of Alexandria c. 185–c. 254 ADAgainst Celsus 1.2

It must also be said in reply to this that the teaching has a proof of its own, more divine than Greek dialectic. This more divine proof the apostle calls a demonstration of the Spirit and of power: of the Spirit, through the prophecies, which are enough to convince the reader, above all in what concerns Christ; of power, through the wonderful mighty works, which must be shown to have happened both from many other considerations and from the fact that traces of them are still preserved among those who live by the will of the Word.

Origen wrote the eight books at Ambrose’s request, answering Celsus’s True Word (written about seventy years earlier) point by point. This is his stated method of proof, before the detailed arguments begin.

Origen of Alexandria c. 185–c. 254 ADAgainst Celsus 2.1

In the first volume of what we have dictated against the work Celsus entitled The True Word, we came to the end of the Jew’s speech, delivered in character, to Jesus. ... Those from the Jews who have believed in Jesus have not abandoned their ancestral law, for they live according to it.

The Jewish charges in books 1 and 2 are not a real Jewish voice: Celsus, a pagan, invented a Jewish spokesman and put the charges in his mouth, and Origen answers that character. Here he opens book 2, which answers the spokesman’s charges against Jews who had believed in Jesus.

Origen of Alexandria c. 185–c. 254 ADAgainst Celsus 3.20

First make clear the letters of the man who said these things, and look closely at the intention of every word in them, for instance the letter to the Ephesians, the one to the Colossians, the one to the Thessalonians, the Philippian letter, and the one to the Romans. Show both things: that you have understood Paul’s words, and that you can point to some simple or foolish people in them. For if he gives himself to reading with attention, I am sure he will either marvel at the mind of the man, who in plain, unlearned speech conceived great things, or, if he does not marvel, he himself will appear ridiculous, whether he explains the man’s intention as if he had understood it, or tries to contradict and overturn what he imagined the man had meant.

Celsus had charged that Christians were uneducated and their teachers without wisdom. Origen answers by sending the critic to Paul’s own letters: the speech is plain, the thought, he argues, is not.