In April 2008 Elder Holland gave a talk, "My Words...Never Cease" about ongoing revelation. In it he also gave a brief history of the Bible. In October 2007 Elder Nelson spoke on Scriptural Witnesses. In April 2007 Elder Ballard spoke about The Miracle of the Holy Bible.
I'll start with a quote from Elder Holland.
For centuries after John produced his writing [Revelation], the individual books of the New Testament were in circulation singly or perhaps in combinations with a few other texts but almost never as a complete collection. Of the entire corpus of 5,366 known Greek New Testament manuscripts, only 35 contain the whole New Testament as we now know it, and 34 of those were compiled after A.D. 1000.2The Bible did not generally exist in the form it has today until over a thousand years after the Savior's life (although there are very rare copies of the Bible from the 4th century that are similar to what we have today; the Codex Sinaiticus is one example). "The Hebrew Bible-the Old Testament-as Jesus knew it, consisted of from twelve to twenty such scrolls of different sizes. They were never united into what we could call one 'book' until the invention of printing made that possible, in the fifteenth century" (Edgar Goodspeed, How Came the Bible?, p.10 as cited by Robert Millet, Selected Writings of Robert L. Millet, p.5). Committees of scholars and Church leaders decided on what they believed to be the most authoritative and authentic books to include in the Bible. However, the books of the New Testament that are accepted into the modern canon were generally denoted as canonical by about 400 AD (Millet, Selected Writings, p.9).
The fact of the matter is that virtually every prophet of the Old and New Testament has added scripture to that received by his predecessors. If the Old Testament words of Moses were sufficient, as some could have mistakenly thought them to be,3 then why, for example, the subsequent prophecies of Isaiah or of Jeremiah, who follows him? To say nothing of Ezekiel and Daniel, of Joel, Amos, and all the rest. If one revelation to one prophet in one moment of time is sufficient for all time, what justifies these many others? What justifies them was made clear by Jehovah Himself when He said to Moses, “My works are without end, and . . . my words . . . never cease.”4