How is the Hebrew Bible organised?

Answer 1

The order of the Tanakh's books:
The Hebrew Bible follows the chronological order: first the five books of the Torah, since they were given before any of the other prophetic books. Then Joshua, Judges, and Samuel and Kings in that order, since that is chronological. Ruth (and others) could be before Kings, but we keep the Prophets and Writings separate.
After Kings, we have Isaiah, Jeremiah and Ezekiel, which is in chronological order. All three of them lived well after the kings had already started.
The Twelve Minor Prophets, who also lived during the latter part of the era of the Kings, are gathered together in a single book of their own.
Then we have the Writings. Psalms, Proverbs and Job are together since they (and none of the other books) are a specific type of poetry ("Taamei Emet", with special cantillation- trope).
The Five Megillot (Song of Songs, Ruth, Eichah, Kohellet, Esther) are together, in the order in which they're read in the synagogue.
Finally, the books of Daniel, Ezra-Nehemiah and Chronicles were written in the end of the prophetic period.Authorship of the Tanakh:

The Torah (the Five Books of Moses): According to tradition, the Torah was given by God to Moses (Exodus 24:12) in 1312 BCE. Moses taught it to the people (Exodus ch.34), and put it in writing before his death (Deuteronomy 31:24) in 1272 BCE
Nevi'im (the Prophets): Jewish tradition (Talmud, Bava Batra 14b) states that the prophetic books were written by the authors whose names they bear: Joshua, Samuel, Isaiah, Jeremiah, Ezekiel, Hosea, Joel, Amos, etc. Judges is credited to Samuel, and Kings was written by Jeremiah. The prophetic books were written in the time of the prophets, from the 1200s BCE (Joshua) to the 300s BCE (Haggai, Zechariah, Malachi).
Ketuvim (the Writings): Jewish tradition (Talmud, Bava Batra 14b) states that the Writings were written by the authors whose names they bear: Daniel, Ezra and Nehemiah. Ruth was written by Samuel; Lamentations was written by Jeremiah; Psalms was set in writing by King David; Chronicles was written by Ezra; Proverbs, Song of Songs and Kohellet (Ecclesiastes) were written by King Solomon; and Esther was written by Mordecai and Esther. The Writings were written between 900 BCE (Ruth) to the 300s BCE (Esther, Daniel, Chronicles, Ezra and Nehemiah).
Concerning Job, the Talmud states more than one opinion as to when it was written.
Hebrew Bible Canon:

Our tradition is that from the time of the First Destruction, God's presence was no longer felt as clearly as before (see Deuteronomy 31:17-18). In addition, exile is not conducive to prophecy (Mechilta, parshat Bo). At that time, the last of the prophets realized that prophecy would soon cease; and that the dispersal of the Jewish people, plus the almost continuous tribulations from the First Destruction onwards, made it imperative to seal the canon of the Tanakh (Hebrew Bible). The Sages of the time, including the last living prophets, convened a special synod for a couple of decades, which was called the Men of the Great Assembly (Mishna, Avot ch.1). This group, who functioned some 2360 years ago, composed the blessings and the basic prayers of the siddur (prayerbook) and the early portions of the Passover Haggadah, made many of the Rabbinical decrees, and (most importantly) sealed the canon of the Tanakh. It was they, for example, who set the twelve Minor Prophets as (halakhically) a single book, and who set the books of the Tanakh in their traditional order (see Talmud, Bava Batra 14b). It was the Men of the Great Assembly whom Esther had to approach when she felt that the Divinely inspired Scroll of Esther should be included in the canon (see Talmud, Megilla 7a).
Since the sealing of the Tanakh, no Jewish sage has ever claimed prophecy.

Answer 2

The Hebrew Bible, or Tanach (ת×?״ך) is arranged in three sections:

The Torah (תורה)

The Prophets (×?ביאים)

The Writings (כתובים)