How do we know absolutely that the Bible is the infallible and inspired Word of God? How did the Bible as we know it today come into existence?
Entire books have been written on the subject of the inspiration of the Bible. It is unlikely that I will be able to address the subject completely in one short answer, but perhaps this will serve as an introduction to the subject.
As we consider the inspiration of the Bible, let us make clear that it's unacceptable to consider the Bible because some man or some organization declares it is inspired. We all know that men make mistakes and the organizations run by men are equally fallible. Just because someone desires that the Bible be inspired by God does not make it so.
Interestingly, the Bible invites close scrutiny of its claim to be a book written by God. It acknowledges that there are huxsters in the world and that we must be careful regarding who we can believe. "Beloved, do not believe every spirit, but test the spirits, whether they are of God; because many false prophets have gone out into the world" (I John 4:1). Anyone can claim to receive a message from God, but the claim alone is not proof of inspiration.
However, we would expect that any work of God would claim God as its author. There are an endless number of books in the world, yet for most we do not need to consider whether they are inspired by God because most do not claim to be inspired. We do need to consider whether the Bible is from God because it does claim to be inspired. "All Scripture is given by inspiration of God" (II Timothy 3:16).
Christians claim that God is all-powerful and all-knowing. Therefore, a book that was written by such a God would have to be consistent in its message. Uninspired messages contain contradictions in their doctrine. A book by God would be perfectly consistent. In fact, this is offered as a point of proof within the Bible. "If there arises among you a prophet or a dreamer of dreams, and he gives you a sign or a wonder, and the sign or the wonder comes to pass, of which he spoke to you, saying, 'Let us go after other gods' -which you have not known-'and let us serve them,' you shall not listen to the words of that prophet or that dreamer of dreams" (Deuteronomy 13:1-3). Moses stated that a true prophet of God will not deliver a message that contradicts previous messages from God.
Even though the Bible was written by over 40 writers living in different countries over a period exceeding 1,500 years, we find the Bible to be highly unified in its teachings. God is consistently described. Men are described without bias -- it tells of men's righteous acts, but also shows that righteous men sin -- nothing is whitewashed. The ethics presented are clear. Righteousness is commanded and the righteous are commended. Sin and those who sin are always condemned. The distinction between the righteous and the wicked is never blurred.
The Bible is also consistent with known history. Every verifiable fact has been shown to be consistent with recorded history. Its records are so consistent that archealogical sites are located by using the descriptions found in the Bible. This we would expect in a book written by God.
Because God is all-knowing and the Bible was written over a large span of time, the predictions found in the Bible are another way to establish whether the message came from God. Again, the Bible also suggests this method of validation. "And if you say in your heart, 'How shall we know the word which the LORD has not spoken?' - when a prophet speaks in the name of the LORD, if the thing does not happen or come to pass, that is the thing which the LORD has not spoken; the prophet has spoken it presumptuously; you shall not be afraid of him" (Deuteronomy 18:21-22). God is distinquished from man's idols by his accurate and detailed foretellings.
""Present your case," says the LORD. "Bring forth your strong reasons," says the King of Jacob. "Let them bring forth and show us what will happen; Let them show the former things, what they were, that we may consider them, and know the latter end of them; Or declare to us things to come. Show the things that are to come hereafter, that we may know that you are gods; Yes, do good or do evil, that we may be dismayed and see it together. Indeed you are nothing, and your work is nothing; He who chooses you is an abomination" (Isaiah 41:21-24).
"Behold, the former things have come to pass, and new things I declare; Before they spring forth I tell you of them" (Isaiah 42:9).
"Tell and bring forth your case; Yes, let them take counsel together. Who has declared this from ancient time? Who has told it from that time? Have not I, the LORD? And there is no other God besides Me, a just God and a Savior; There is none besides Me" (Isaiah 45:21).
"Calling a bird of prey from the east, the man who executes My counsel, from a far country. Indeed I have spoken it; I will also bring it to pass. I have purposed it; I will also do it" (Isaiah 46:11)
The evidence of the prophecies found in the Bible are large in quantity and solid in their accuracy. For example, in Isaiah 44:28, the name of the king who would free Judah from captivity is recorded 150 years in advance of the actual event. Some deny this plain evidence, claiming that the record was added after the fact, but historical evidence reveals they are wrong. But there is another record that cannot be avoided. Isaiah 52:13-53:12 gives a detailed account of the Christ. It was written about 700 years before Jesus came to this earth and we have physical copies of Isaiah that are dated to 200 years before Jesus' birth. Yet the record is accurate to the smallest detail. Or consider Psalms 22:12-18, a psalm composed by David nearly 1,000 years before Jesus' death, yet it contains precise details regarding how Jesus died. These accounts could not have been made true by believers because many of the details required the unknowing participation of non-believers.
Peter claimed that the Bible would survive because it is God's book. "Since you have purified your souls in obeying the truth through the Spirit in sincere love of the brethren, love one another fervently with a pure heart, having been born again, not of corruptible seed but incorruptible, through the word of God which lives and abides forever, because "All flesh is as grass, and all the glory of man as the flower of the grass. The grass withers, and its flower falls away, but the word of the LORD endures forever." Now this is the word which by the gospel was preached to you" (I Peter 1:22-25).