I brought up this question with my freshman students this last class period, and the first answer they gave was, "read the Bible."
There are multiple reasons why this was not the primary answer given in the early church.
In order to read the Bible several conditions have to be met:
1) There has to be a Bible. Though all of the books of the NT had been written, there was no canon per se. Part of the whole controversy is deciding which books were authoritative and which were not.
2) You have to be able to read, which most of the early Christians could not.
3) If you can read, you have to also have enough money to buy a copy of the scriptures, or pay a copyist to copy one for you. You couldn't just walk down to Barnes and Noble and pick up a copy of the Bible.
And one more reason why scripture did not automatically guard right belief was that the heretics used scripture just as much as the orthodox did.
Therefore, where early Christians turned more often amidst debates about doctrine were the church leaders. Careful consideration was given to appointing church leaders who could faithfully carry on right teaching. Even more than this, there was some emphasis put on who discipled certain leaders. This led to an emphasis on apostolic succession. In its most basic form, this meant that one could trace a certain leader's spiritual lineage back to one of the disciples. In a very specific form this meant that one leader could trace back his discipleship lineage to Peter, the original "Bishop" of Rome.
Interestingly, though in its Roman Catholic form, this appeal to authority is often thought to be a later development. Indeed, in say the second century one cannot even speak of a Roman Catholic Church in the same sense as it existed after Constantine. Yet, the seeds of this appeal to the authority pf the bishop of Rome has very early roots. Consider Irenaeus, late 2nd century, who listed the first thirteen Bishops of Rome, including Peter himself. Irenaeus writes:
3. The blessed apostles, then, having founded and built up the Church, committed into the hands of Linus the office of the episcopate. Of this Linus, Paul makes mention in the Epistles to Timothy. To him succeeded Anacletus; and after him, in the third place from the apostles, Clement was allotted the bishopric. This man, as he had seen the blessed apostles, and had been conversant with them, might be said to have the preaching of the apostles still echoing [in his ears], and their traditions before his eyes. Nor was he alone [in this], for there were many still remaining who had received instructions from the apostles. In the time of this Clement, no small dissension having occurred among the brethren at Corinth, the Church in Rome dispatched a most powerful letter to the Corinthians, exhorting them to peace, renewing their faith, and declaring the tradition which it had lately received from the apostles, proclaiming the one God, omnipotent, the Maker of heaven and earth, the Creator of man, who brought on the deluge, and called Abraham, who led the people from the land of Egypt, spoke with Moses, set forth the law, sent the prophets, and who has prepared fire for the devil and his angels. From this document, whosoever chooses to do so, may learn that He, the Father of our Lord Jesus Christ, was preached by the Churches, and may also understand the tradition of the Church, since this Epistle is of older date than these men who are now propagating falsehood, and who conjure into existence another god beyond the Creator and the Maker of all existing things. To this Clement there succeeded Evaristus. Alexander followed Evaristus; then, sixth from the apostles, Sixtus was appointed; after him, Telephorus, who was gloriously martyred; then Hyginus; after him, Pius; then after him, Anicetus. Soter having succeeded Anicetus, Eleutherius does now, in the twelfth place from the apostles, hold the inheritance of the episcopate. In this order, and by this succession, the ecclesiastical tradition from the apostles, and the preaching of the truth, have come down to us. And this is most abundant proof that there is one and the same vivifying faith, which has been preserved in the Church from the apostles until now, and handed down in truth. (Irenaeus, Against Heresies, 3.3.3).Interesting stuff!