I recently read through Karen Armstrong's The Bible: A Biography (2007). The first two chapters, titled "Torah" and "Scripture," review current scholarship on how the Jewish Bible (aka "the Old Testament") came to be, which makes a good review for the upcoming year of studying the Old Testament in LDS Sunday School. Scholarship does not, of course, define the LDS view of the Bible, but it can help us recognize various questionable Protestant beliefs about the Bible that often get amalgamated with LDS views.
Rather than try to summarize fifty pages, I am going to just highlight a few general concepts and ideas that emerge from these two chapters, adding quotations when helpful.
1. The Jewish Bible is rooted in the 6th century exile in Babylon. Before exile, political life in Judah was directed by the monarchy and religious life by the temple and its priests. In exile, these pillars of Israelite life were removed. To preserve their religious identity, the exiles focused on gathering, editing, and studying the sacred texts that they carried with them when they left Judah. The overarching question, of course, was why God allowed this national disaster to come upon them and what it all meant.
2. The texts were not yet fixed. In exile, priests who formerly ministered at the temple became scribes and scholars ... what else could they do? They edited and rewrote the received texts with an eye to understanding the present condition of the people of Israel: no king, no temple, and no land of their own.
[I]t would be many years before Yahwism [Judaism] became a religion of the book. The exiles had brought a number of scrolls from the royal archive in Jerusalem with them to Babylon, and there they studied and edited these documents. ... But the scribes did not regard these writings as sacrosanct and felt free to add new passages, altering them to fit their changed circumstances. They had as yet no notion of a sacred text. (p. 11.)
3. One view of Israelite religious history: the Deuteronomistic reformers of the late 7th century. This reform movement dates to the discovery of a scroll of the law in the temple (1 Kings 22) and the resulting reforms instituted by good king Josiah (1 Kings 23).
Hilkiah [a priest] and Shaphan [a scribe] claimed that this scroll had been lost and its teachings never implemented .... Hilkiah's document probably contained an early version of the book of Deuteronomy, which described Moses delivering a "second law" ... shortly before his death. But instead of being an ancient work, Deuteronomy was an entirely new scripture. It was not unusual for reformers to attribute new ideas to a great figure of the past. The Deuteronomists believed that they were speaking for Moses at this time of transition. In other words, this was what Moses would say to Josiah if he were delivering a "second law" today. (p. 22.)
This reformist view dominates Deuteronomy and the historical narrative that runs from Joshua through 2 Kings.
The reformers did not use their scripture to conserve tradition, as is often done today, but to introduce radical change. They also rewrote the history of Israel, adding fresh material that adapted the JE epic to the seventh century, paying special attention to Moses, who had liberated the Israelites from Egypt, at a time when Josiah hoped to become independent of Pharoah. ... They also wrote a history of the two kingdoms of Israel and Judah in the books of Samuel and Kings, arguing that the Davidic monarchs were the only legitimate rulers of the whole of Israel. Their story culminated in the reign of Josiah, a new Moses and a greater king than David. (p. 23.)
4. A second view of Israelite religious history: the priests and scribes of the 6th century. The Deuteronomists celebrated a strong monarchy that would aggressively and even violently purify Judaism from competing influences. But priests and scribes in exile developed, then championed, a kinder and gentler view of Israelite history.
[S]ome of the priests, who in losing their temple had lost their whole world, looked back to the past and found a reason for hope. Scholars call this priestly layer of the Pentateuch "P", though we do not know whether P was an individual or, as seems more likely, an entire school. P revised the JE narrative [in Genesis and Exodus] and added the books of Numbers and Leviticus, drawing upon older documents — genealogies, laws and ritual texts — some written down, others orally transmitted. ... Some of P's material was very old indeed, but he created an entirely new vision for his demoralized people. (p. 25-26.)
A key component of the priestly vision was holiness, which included treating strangers and foreigners with love and kindness (in contrast to the Deuternomists, who were cheering for Josiah to extend Israelite political power by conquest and subjection of neighboring peoples).
Holiness also had a strong ethical component. Israelites must respect the sacred "otherness" of every single creature. Nothing could be enslaved or possessed, therefore, not even the land. Israelites must not despise the foreigner: "If a stranger lives with you in your land, do not molest him. You must count him as one of your own countrymen and love him as yourself — for you were once strangers in Egypt." (p. 27.)
5. Add the prophets and you have a Bible. Cyrus the Persian allowed the exiles to return; some did, and they took their writings with them. The writings were still scrolls, not yet an ordered and defined collection of books.
Towards the end of 539 ... a small party of exiles set out for Jerusalem. ... The returning exiles brought home nine scrolls that traced the history of their people from the creation until their deportation: Genesis, Exodus, Leviticus, Numbers, Deuternonomy, Joshua, Judges, Samuel and Kings; they also brought anthologies of the oracles of the prophets (neviim) and a hymn book, which included new psalms composed in Babylon. It was still not complete, but the exiles had in their possession the bare bones of the Hebrew Bible. (p. 30.)
6. Ezra, 4th century scribe and reformer. The new Jerusalem community soldiered on, eventually rebuilding a smaller and humbler version of the destroyed temple, then stagnating. Then, early in the 4th century, Ezra came from Babylon to Jerusalem. He was another reformer who energized the community by revising the inherited stock of sacred writings. "When he arrived in Jerusalem, he was appalled by what he found. The people were not maintaining the holy separation from the goyim that P had prescribed: some had even taken foreign wives" (p. 33). And so forth. Ezra's response was to teach these frontier Jerusalemites the Torah as he, the sophisticated and scholarly Babylonian Jew, understood it.
Standing on a raised wooden dais, he read the text aloud, "translating and giving the sense, so that the people understood what was read," while Levites versed in the Torah circulated among the crowds, supplementing this instruction. We are not sure which laws were proclaimed on this occasion, but, whatever they were, the people had clearly never heard them before. (p. 33.)
It seems the proto-biblical writings the exiles took to Jerusalem had continued to evolve in Babylon. This "traditioning process" whereby prophets, priests, and scribes periodically update inherited scripture to meet the needs of a new time and place never really stops. In LDS terms, this might be described as a "likening unto us process." We generally think of this as the oral interpretation of fixed written texts, but in earlier times, at least through the time of Ezra, the process also included updating and rewriting fluid written texts. This opens up a much different approach to understanding the Bible than the "original autographs" and closed canon assumptions that direct the thinking of most conservative Protestants.
That's enough for now. A similar account with more detail is found in Richard Elliott Friedman's Who Wrote the Bible?