Which Christians are you referring to? Who decided which ones?
The Pauline epistles came to be accepted pretty early, by the time anyone was even talking about what books should be read in the churches at all, the letters of Paul were largely an assumed given. Figuring out exactly when Paul's letters became so widely accepted is difficult to pinpoint, the dating of 2 Peter can be helpful given the comments made in the text, but certainly by the mid 2nd century to the last quarter of the 2nd century a proto-New Testament Canon consisting of what is typically called the homologoumena was in place, an an early attestation to the discussion between homologoumena and antilegomena can be seen in the Muratorian Fragment usually dated to around the year 200. Though we can see earlier references to certain books among the 2nd century fathers such as Justin and Irenaeus. Taking the dating of 2 Peter (one of the books of the antilegomena) is helpful. A date between about 90-130 AD is probably reasonable for the dating of 2 Peter, thus making it contemporary with the Apostolic Fathers, (e.g. Clement of Rome, Ignatius, Polycarp, et al).
There was no real formal process for how the New Testament Canon came to be, the process was long and largely informal; coming about through a gradual and growing consensus of the Faithful. Certain leaders in the Church gave their opinion, and those opinions carried weight, but those opinions were also usually governed by what was largely already widely accepted and happening in the churches themselves. So it wasn't exactly a top-down process, but was largely a ground-level process--widespread usage and acceptance in the regular worship happening around the Christian world being engaged with and by various leaders within the Church, and in later centuries local councils also weighing in (e.g. the Councils of Carthage, Hippo, and Laodicea, which did not all agree with each other concerning the Canon, but which were influential in the ongoing process).
Because, and this is important, what is called the Bible today is the result of what books were to be read in the churches, that is, what was to be read out loud as part of the liturgy. When we see statements concerning books that should be read and books that shouldn't be read this isn't about personal reading, as though there were books that someone simply was banned to ever look at; rather it was about what was to be read out loud as part of organized Christian worship. Then, as now, Scripture readings are a fundamental component of ordinary Christian worship. The Bible, then, developed as a
liturgical document.
And because the Canon developed in this way, what is to be regarded as Scripture is determined by the historic usage and widespread acceptance within the Church; so even if we, today, came across a copy of the long lost Book of Jasher, or the Book of Ido the Seer, these would never be part of the Canon, they would not be Scripture. Because what is and isn't Scripture is the result of two thousand years of inter-Christian discussion and consensus. Nobody ever read Jasher or Ido in the churches, it was never part of normative Christian worship, they therefore simply are not--should they ever be discovered--ever going to be part of the Christian Canon of Scripture. Not as far as mainstream, orthodox Christians are concerned anyhow.
-CryptoLutheran