Who was the author? Moses's aide and successor Joshua, son of Nun, is generally held to have been Divinely inspired to write most of the book that bears his name, although the final verses of the book may have been written by others, who may also have done some editing.
What is the book? The book of Joshua is the first of the so-called "Former Prophets" and tells Israel's history from a prophetic standpoint, continuing the Old Testament historical narrative from where Deuteronomy left off and taking it up to the events of Judges.
Where was it written? If Joshua wrote the book that bears his name, we might reasonably think that he wrote it in the town he asked for, Timnath Serah in the hill country of his tribe Ephraim (Joshua 19:50).
When was it written? An approximate date for Joshua's death is 1375 B.C., so we would probably say the book was written around that time.
Why? The book of Joshua does more than simply give historical events; the book tells of God's faithfully acting through those historical events, despite the people's unfaithfulness, to fulfill His promises to Moses and all the children of Israel by bringing them into the Promised Land, delivering them from their enemies, and always pointing to the greater Prophet and Deliverer, Jesus Christ, Who brings the Israelites and us to the greater rest of heaven.
How? Joshua himself is a living prophecy of the God-man with the same name (the Hebrew "Joshua" is equivalent to "Jesus" in Greek). The pre-incarnate Lord may appear in the events of the book, and there are other details that also point to Jesus's redeeming us by His blood shed on the cross.
For further reading on the book of Joshua:
- Harstad, Adolph L. Joshua, Concordia Commentary: A Theological Exposition of Sacred Scripture. Saint Louis, Missouri: Concordia Publishing House, 2004. (I don't own this volume, but my general experience with this new series of commentaries is that it is scholarly but also accessible. You can see the volume on Joshua's catalog description here.)
- Keil, C.F. and F. Delitzsch. Biblical Commentary on the Old Testament, Volume II: Joshua, Judges, Ruth, I & II Samuel, translated by James Martin and published as two volumes in one. Grand Rapids, Michigan: William B. Eerdmans Publishing Company, reprinted August 1985. (The section dealing with Joshua runs 236 pages. After my study Bible, this is what I turn to next, but it is a somewhat harder to use more-scholarly commentary, that is a bit dated in terms of modern scholarship.)