How were the prophecies of Biblical prophets such as Isaiah first published or disseminated?

Our understanding of the composition and redaction of biblical texts has developed enormously over the course of the 20th century alone - let alone since the days in which Isaac Newton published his Observations! The ascription to Ezra of the editing process (while not an invention of Newton's) reflects on a general tendency to ascribe authorship to characters within the corpus. The popular perception that the book of Isaiah was written by a person named Isaiah owes its origin to this same tendency.

So who did write Isaiah? And when did the author live? (I know that your question only uses Isaiah as an example, but it's a paradigmatic one, so I'm going to stick with it.)

A careful reading - in fact, even a not very careful reading - is sufficient to tell us that there are at least two different books called Isaiah. Chapters 1-39 are all clearly set in the 8th century BCE. They make reference to 8th century BCE kings and empires, and indicate them by name. When Isaiah rails against Sennacherib in chapters 36 and 37, he is clearly speaking about somebody at least reasonably contemporary. The climax, in chapters 38-39, tells of the healing of Hezekiah and the securing of peace.

Chapters 40-66, on the other hand, are very obviously written some two hundred years later, in the 6th century BCE. Not only do they make reference to 6th century BCE kings (to the exclusion of 8th century BCE kings, who are never mentioned after chapter 39), but they name them. This section of the text also presupposes an awareness of the Babylonian captivity, which commenced after Babylon's invasion of Judea in c.598 BCE.

The disparity between these two sections has long been known; anybody who reads the text and knows a smattering of history will notice it. The Talmud, for example, goes to very creative lengths to demonstrate that Isaiah (who was, after all, a prophet) foresaw Cyrus the Great and included him in his text, and that Cyrus was so flattered by his having been prophesied that he saw fit to fulfil the prophecies that were spoken of him. Contemporary scholars would argue, on the other hand, that there is more than one "Isaiah".

Once we recognise this, we can then realise that Isaiah is also more genre than individual. Different people can write Isaianic oracles, and the book so known is but an amalgamation of the work of a school. The same thing could be said for Jeremiah and Ezekiel, and certainly for Daniel. (The Greek translation of Daniel features an additional two stories that are not found in the Hebrew).

There is plenty of evidence from within the Bible that prophets belonged to guilds and that they took students. These students were known as "the sons of prophets" - hence the declaration that a certain widow's late husband was one of the sons of the prophets (2 Kings 4:1), or Amos' statement to the effect that he is neither a prophet nor the son of one (Amos 7:14). [Note: this is an example of biblical parallelism: being a prophet and being "the son of a prophet" are both the same thing.]

So if the prophets comprised schools, and if their oracles, while associated with a particular individual's ministry, were not necessarily written by the individual so named, then what was the function of this literature?

As oracles, their purpose was instructional. The heavy emphasis on social justice found throughout these texts, coupled with the fact that they all spoke truth to power and that several of them suffered as a result, would seem to suggest a hortatory purpose - like wandering preachers. Some of them, like Jeremiah, may have had their own scribes, but the works attributed to them are too finely crafted to be a faithful reflection of what was said in the moment.

As literature, so compiled and edited together, these books served a similar purpose to the other books within the corpus and were transmitted in the same ways: pieces of writing, circulating amongst elite scribal groups that saw fit to preserve text, later to be edited into a corpus that would include by association various other texts, all deemed scripturally authoritative in some fashion. In later years, sections from the prophets would be read weekly in synagogues, together with passages from the Pentateuch.

While the texts of the Bible are all different from one another, they all have in common the idea that human history has divine authorship: there is a plan for God's people, and that all will go well for them if they uphold their side of the bargain. Since there is not a single text within the Bible that was written with the intention that it would become part of a bible, by grouping these books together we create a false consensus. As such, it is hard to read Isaiah (for example) and not do so in light of, for example, Leviticus.

In a text like that one, maintaining "our" side of God's bargain is done through the careful observation of law. But for the prophets, we maintain our contract with God by supporting the poor and the indigent. A society shows its true colours, they would argue, by how it responds to its most vulnerable members. Such was the purpose of their prophecy, and such was no doubt also the purpose of preserving it.