In terms of meetings in the early church were church leaders decided on which books would be in the New Testament, such meetings didn’t really exist. There was no definitive assembly were some books were canonized and others discarded. Rather the church gradually came to recognize which first century books comprised the canon of the New Testament (the Old Testament canon that was accepted and used by the early church was for all intents and purposes the same list of books comprising the Hebrew Tanakh read in the Synagogue, although most Christians used the Greek Translation of the Old Testament known as the Septuagint or LXX). The evidence is that even as most of the books of the NT were being written and distributed in the first century (especially the epistles or letters of the Apostles) they were accepted by the church as inspired Scripture. For instance, Paul directs that his letters be read in the churches, and Peter calls the letter of Paul “scripture” (2 Peter 3:15-16). Certainly some later church councils published lists, but these were merely recognizing what the church had already known and practiced for some time.

Thus the early lists of books from the mid 100s (the Muratorian, Tertullian, etc.) - that list the books read in the 2nd century churches were essentially made up of the same list of books we have in a modern New Testament. Admittedly there were some disputes over certain books that were being circulated, such as Hebrews and thus you don’t find them in every list, but the only list that doesn’t contain all four gospels (Matthew, Mark, Luke, and John) is the abridged list of Marcion, the leader of a Gnostic second century cult that only accepted Luke and Paul’s Epistles (Marcion also dismissed the entire Old Testament claiming the God of the OT was a different God).

The books that you find in the modern New Testament were all first century works, generally dating from a period spanning almost 50 years from about 50 AD through 98 AD. Some of the letters of Paul are the earliest books in the NT and the oldest is the Revelation of John. As far as the authenticity of the text is concerned, this is confirmed in that whenever we find an old papyri, such as the early 2nd Century Chester Beattie Papyri which is a fragment of John, the text matches up with what we have.

Now, you’ve probably heard of other Gospels such as the “Gospel of Thomas.” Dan Brown wrongly identifies these as part of the “Dead Sea Scrolls” in the Da Vinci Code. The Dead Sea Scrolls were something entirely different, they were an Essene collection of Old Testament and Intertestamental books discovered in Wadi Qumran in Israel. These other gospels largely come from Nag Hamadi in Egypt and were written in the Second and Third centuries by Gnostics under assumed names (Gnostics like Valentinus for instance knew that writing under the name of an Apostle gave more credibility than writing as a Gnostic). The important thing to note is that these books were written well after the first century (no one disputes this) by promoters of Gnosticism, a Greek mystical philosophy that promoted a view that the physical or material world was inherently bad and that the spirit was good and that one obtained release from the material world via the knowledge of “secret teachings” (hence gnosis meaning knowledge). In some respects their philosophy of salvation or enlightenment via the secret teachings of ascended masters is akin to that of the Theosophists, Christian Scientists, and Scientologists. These Gnostic gospels were never accepted as genuinely canonical outside of localized Gnostic cults, and when the cults disappeared the writings ceased to be circulated. Today they are gaining attention because as in the second and third century, many people are unhappy with the historical Jesus taught in the first century works.

In any event, by the time Nicea met, the modern list of the books of the NT was well accepted throughout the church. Some may, like Gnostics ancient and modern, not like or agree with those books and what they taught, but they are what the Apostles witnessed and the church believed.

As for scholarly sources on the accumulation of these books, please check out:
http://www.monergism.com/directory/...n-of-the-Canon/