The development of the biblical Canon has taken place over the course of most of the last two thousand years.
The earliest Christians in general received those Scriptures which were in general accepted at the time; largely that meant the Septuagint. The Septuagint (also known as the LXX) is/was, according to the tradition, a translation originally made a few centuries before Jesus by a group of around seventy Jewish scholars living in Alexandria. The translation was made from Hebrew/Aramaic into Greek. This Greek translation of Jewish Scripture was easily received into the earliest Christian communities because Greek was the common language of the Roman Empire--it was the language of trade, commerce, politics and religious debate and communication.
These earliest Christian communities relied heavily upon these Scriptures as well as the verbal teaching of the Apostles (those sent out by Christ to the nations). One of the most important figures in the early Christian movement was Paul of Tarsus, a Pharisee-turned-Christian apostle due to a dramatic experience where he claimed to have encountered the risen Jesus and then became the most well known champion of the fledgling Jesus Movement.
Paul helped found several communities and also encouraged others with the help of many others, including Barnabas, Silas, as well as those among the Twelve (the core group of Jesus' disciples and apostles). Something Paul was prolific about was writing letters, he wrote to many of the early communities about many different topics relevant to those individual communities.
These early communities preserved many of his letters and began to circulate them and they began to be read in church communities other than the original recipients.
Further, these earlier Christian communities started to put the Jesus story which they had received down in writing, these became the Four Gospels.
Other early Christians also wrote material, mostly letters to individuals and groups of people. Other kinds of writings were also produced, apocalyptic material such as the Revelation of John, the Revelation of Peter, and the Shepherd of Hermas. They wrote down basic instruction and teaching (such as the Didache).
From early on there was a core group of Christian writings that began to be read alongside "the Scriptures" (aka the Septuagint). Mostly the letters of Paul and the Four Gospels, but there were others: several letters by John the Elder (who may or may not be John the Apostle), a couple by Peter, and so on.
Eventually Christian leaders started discussing what is proper to be read in the churches and which isn't. By the end of the second century the beginnings of a New Testament begins to take shape with a group of books that were nearly unanimously agreed to be Scripture: The Four Gospels, the Letters of Paul (including Hebrews), one letter of John, one letter of Peter, and the Acts of the Apostles.
There were other books that were commonly read but there was some dispute over their appropriateness and/or authenticity: A second letter of Peter, two other letters of John, a letter of Jude, a letter of James, a letter of Barnabas, the Shepherd of Hermas, the Didache, two letters of Clement, an apocalypse by John (the Revelation of John), and an apocalypse by Peter. This list of books were generally known as Antilegomena, that is, they were disputed.
Contrary to some claims made by shoddy scholars on the internet and in poorly researched books, there was no large action to remove books, nor were the books which became today's New Testament a decision made by a single group of clergy. Even with various regional church councils in the fourth and fifth centuries there continued to be debate as to the value and authority of several of these books.
The Armenian Bible at one time contained a 3rd Corinthians. The Latin Vulgate even into the middle ages contained an epistle to the Laodiceans. In the 8th century a lot of the churches in the East continued to struggl to accept the Revelation of John. One of our most important biblical codices from the 5th century contains the Didache, the Epistle of Barnabas and 1 Clement.
The New Testament has come down to us in the present largely as a result of general consensus. There has never been a truly ecumenical council--that is a concerted effort for a pan-Christian exercise to define the Bible once and for all--and as such there continues to be disagreement among Christians on exactly what belongs in the Bible and what doesn't. Case-in-point: Most Protestants don't have the Deuterocanonicals in their Bible, whereas Catholics and Orthodox do (and Orthodox have even more of them than Catholics).
At the end of the day the Bible isn't the end-all or be-all of Christianity, but is the received collection of Sacred and Holy Scripture (even if we disagree on a lot of the details) which guides us toward God and in our faith in Jesus. After all, the Christian confession is that God's True Word is ultimately a person, not a book or collection of books.
-CryptoLutheran