How, when, who & how long did it take to compile all the writings of the Bible into the one Bible book as we know it today? What determined its order?

Actually, even though the Old Testament is the larger part, that was a much easier transition from Jewish Scriptures to Christian bible. Keys to the books of the Old Testament being included in the Bible were both the sacred history that was being told and also the power that was evident whenever those books were read. Another key was also consideration of the writers themselves—specifically their relationship to God. The first five books (the Pentateuch, also called the books of the Law)—Genesis, Exodus, Leviticus, Numbers and Deuteronomy—were considered the basis of the Hebrew faith. They were considered sacred scriptures because they were written by Moses. The books of the prophets were both studied and quoted in Hebrew worship, and were included because their authors (Isaiah, Jeremiah, etc.) were considered direct spokesmen for God. The Old Testament Scriptures were written by about 31 different authors and spanned approximately 1,100 years of history (1500-400 BC). There were various councils or committees that discussed their responsibilities both for maintaining the manuscripts (and their accuracy) and the passing down of these manuscripts to the next generations. By about 400 BC, the books considered sacred and therefore authoritative scripture were pretty much in place. The Jewish Council of Jamnia (90-118 AD), confirmed both which books should be considered Scriptural and, just as important, which books should not. It was at this council that Jewish authorities officially rejected the books we know as the Apocrypha, which ultimately, by decree of the Council of Trent (1545-1563), became included in Catholic bibles and thus, by extension, gave scriptural “support” to questionable Catholic doctrines following the Protestant Reformation.
The New Testament, written by probably nine different authors (Hebrews is the one unknown regarding authorship), is written over much shorter span of time—probably no more than 40 or so years (48-90 AD). The standard for inclusion was very precise: Had the author had personal experience with Jesus Christ? In other words, was he considered an apostle? Apostolic authority and/or connection was the standard. Well, Matthew was one of the 12 original disciple of Jesus. Mark is considered because of his longstanding connection with the apostle Peter, from whom Mark is thought to have gotten his material. Luke, while not an apostle, was the traveling companion to Paul, who was certainly considered directly connected to Jesus. John was one of the 12 original disciples of Jesus. Paul was viewed as an apostle, and wound up writing almost half (13) of the 27 books in the New Testament. Hebrews is the one with the mystery author, but Hebrews places huge reliance on the scriptures of the Old Testament to validate the purpose of the atoning sacrifice of Jesus Christ. James was the half-brother of Jesus and leader of the Jerusalem church. Paul specifically tells us that, following his resurrection, Jesus appeared to James. Peter, of course, was one of the 12 original disciples of Jesus. And Jude (also known as Judas) was also a half-brother of Jesus. What is also interesting, though more subjective, is that the books accepted as part of our New Testament have largely been regarded as Scripture by the body of believers of the early church. By about 100 AD, the same gospels we recognize were unofficially viewed as a set. By 120 AD, the epistles of Paul had been likewise viewed as a collection. By 145 AD, a church council recognized essentially the same books as making up the New Testament as we know today. And by church councils meeting in 397 AD (Carthage) and 400 AD (Hippo), our New Testament was essentially established. But even before that, the first century church understood that the materials being written at the time were meant to be as much a part of the Scriptural story as the Old Testament they knew. In his first letter to Timothy, the apostle Paul quoted from both the Old Testament (Deuteronomy) and from Luke’s account of the life of Christ, and calls them both “scripture”: The elders who direct the affairs of the church well are worthy of double honor, especially those whose work is preaching and teaching. For Scripture says, “DO NOT MUZZLE THE OX WHILE IT IS TREADING OUT THE GRAIN,” and “THE WORKER DESERVE HIS WAGES”—Paul, I Timothy 5:17-18 (quoting Deuteronomy 25:4 and Luke 10:7). Paul is equating Luke (even as he quotes Jesus) with the already-established scriptural view of Deuteronomy—that this is God’s word. This is an amazing viewpoint, considering that Luke’s gospel was essentially a newly-written work (about three years old), and even the quote from Christ would have been only about 30 years old. Not only that, but Peter in his second letter equated Paul’s words as scripture: Bear in mind that our Lord’s patience means salvation, just as our dear brother Paul also wrote you with the wisdom that God gave him. He writes the same way in all his letters, speaking in them of these matters. His letters contain some things that are hard to understand, which ignorant and unstable people distort, as they do the other Scriptures, to their own destruction—II Peter 3:15-16. And, of course, Paul even in his own time recognized the ultimate Author of the words he had written, which he mentions several times. Toward the end of his first letter to the church at Corinth, as he concludes writing about spiritual gifts, he says, If any thinks he is a prophet or spiritually gifted, let him acknowledge that what I am writing to you is the Lord’s command—Paul, I Corinthians 14:37. And certainly the One who authored his written words also authored his spoken ones; as he shared with the Thessalonian church, And we also thank God continually because, when you received the word of God, which you heard from us, you accepted it not as the word of men, but as it actually is, the word of God, which is at work in you who believe—Paul, I Thessalonians 2:13.
Ultimately, for all the books that became our Bible, people asked five questions: (1) Was the book written or backed by a prophet or apostle of God? In other words, the Word of God which is inspired by the Spirit of God must be communicated through a man of God. God Himself stated this view: I will raise up for them a prophet like you from among their brothers, and I will put my words in his mouth, and he will tell them everything I command him—God speaking, Deuteronomy 18:18. The apostle Peter underscored this fact, telling his readers, Above all, you must understand that no prophecy of Scripture came about by the prophet’s own interpretation. For prophecy never had its origin in the will of man, but men spoke from God as they were carried along by the Holy Spirit—II Peter 1:20-21. (2) Is the book authoritative? Remember how people reacted following the Sermon on the Mount and, in fact, all the great times that Jesus spoke? When Jesus had finished saying these things, the crowds were amazed at his teaching, because he taught as one who had authority, and not as their teachers of the law—Matthew 7:28-29. The books of God should speak with the same authority as the Son of God—an authority that challenges people, that confronts people, that changes people. (3) Does the book tell the truth about God as it is already known by previous revelation? Remember how the Bereans reacted when Paul came to their town preaching Jesus? Luke tells us: Now the Bereans were of more noble character than the Thessalonicans, for they received the message with great eagerness and examined the Scriptures every day to see if what Paul said was true—Acts 17:11. They searched previous revelation of God to confirm Paul’s revelation of God in Jesus Christ. They knew the Scriptures they had were true, and they used that standard and measure of truth to judge Paul’s words. (4) Does the book give evidence of having the power of God? The author of the book of Hebrews defined the power of the Word of God like this: For the word of God is living and active. Sharper than any double-edged sword, it penetrates even to dividing soul and spirit, joints and marrow; it judges the thoughts and attitudes of the heart—Hebrews 4:12. And Paul in his letter to his protégé Timothy said, But as for you, continue in what you have learned and have become convinced of, because you know those from whom you learned it, and how from infancy you have known the Holy Scriptures, which are able to make you wise for salvation through faith in Christ Jesus. All Scripture is God-breathed and is useful for teaching, rebuking, correcting and training in righteousness, so that the man of God may be thoroughly equipped for every good work—Paul, II Timothy 3:14-17. The power of God, particularly His power to change lives, should be evident in His Word. And finally: (5) Was the book accepted by the people of God? In the Old Testament, we know that Moses equated his writings with God’s Word because [a]fter Moses finished writing in a book the words of this law from beginning to end, he gave this command to the Levites who carried the ark of the covenant of the Lord: “Take this Book of the Law and place it beside the ark of the covenant of the Lord your God. There it will remain as a witness against you—Deuteronomy 31:24-26. Joshua did something similar with his writings at the end of his life. In the New Testament, Paul’s letters were circulated from one church to another; he gave instruction to the Colossian church that [a]fter this letter has been read to you, see that it is also read in the church of the Laodiceans and that you in turn read the letter from Laodicea—Paul, Colossians 4:16, very similar to what he said to the Thessalonian church: I charge you before the Lord to have this letter read to all the brothers—Paul, I Thessalonians 5:27. Historically, the Holy Spirit seemed to have directed the churches as to what was true and worthy of teaching, as usage within the churches seemed to overwhelmingly endorse what books constituted the Scriptures.
As to order, the first five books of the Old Testament were so foundational to Jewish thought that they were an obvious choice to lead, plus they were in real time the first written. The historical books logically came next (Joshua through Esther), telling the story of how God’s law was (or was not) fleshed out in real life. The poetical and wisdom books reflect man’s thoughts on dealing with God and His standards, and the prophetical books record men of God calling a wandering nation (Israel) back to God. In real time, the historical books of Ezra and Nehemiah and the prophetic book of Malachi are considered the last ones actually written, with Malachi closing out the Old Testament. In the New Testament, since it is all about the impact of God in human form coming to earth, it’s only appropriate that the gospels come first, along with the story of the church Jesus founded. Following that are the epistles (Pauline and otherwise) which talk both theology and practicality as that church attempts to move forward while confronting several challenges to its existence. Finally, the great hope of God’s eventual triumph through Christ and all history being closed out concludes with Revelation (also the last book written in real time). Thematically, the order of the Bible makes tremendous sense.