God dictated the Bible to men from ancient times to the first century A.D.
There is some disagreement on whether the first part written down is the Ten Commandments (written by God’s own hand and given to Moses; the most popular view) or if Adam and his descendants actually wrote the parts of Genesis concerning their own lives and Moses later compiled them into one book.
Either way, God then dictated the next four books to Moses. These first five books are called the Pentateuch (literally- “five books.”). Job is believed by many to be a contemporary of these books.
The rest of the Old Testament was finished and pretty much in the form we know it today (though in ancient Hebrew, not English of course) by 400BC. Scribes painstakingly copied the originals checking letter for letter, destroying entire panels if they got even two letters too close together. This attention to detail was carried into the Greek Septuagint (literally "Seventy" Ptolomy I, who ruled Egypt after the death of Alexander the Great, asked Judah [post Babylonian Captivity] to send men to translate the Hebrew Law into Greek so it could be included in the Library of Alexandria. Judah sent six from each tribe. The "Septuagint" is the result. "Seventy" is easier to say than "Seventy-Two.").
We know the most ancient copies, then, are accurate.
For even more verification, the Dead Sea scrolls were discovered in the mid 1900’s. These are documents written between 150BC and 70AD including many of the books of the Old Testament. Some of these have been translated into modern languages with the discovery that our current Bible matches exactly.
The New Testament was completed (in Greek) by the end of the first century A.D. The churches and their leaders agreed that certain letters and documents were valuable to all the churches and made exact copies to share with each other. These were assembled into the New Testament.
We still have some of the writings of the second generation of church leaders, those taught directly by Jesus' disciples. These men often quoted from what we call “The New Testament,” and their quotes translated into modern English confirm what we have as the original letters written by the Apostles. In fact, we could assemble the entire book of John just from the quotes in the works of Augustine!
The most ancient copies of the complete Bible we have today are the Codex Alexandrius and the Codex Sinaiticus in the British Museum Library in London, and the Codex Vaticanus in the Vatican. They date back to approximately the 300’s AD.
In 382AD, Saint Jerome, translated the New Testament from its original Greek into Latin. This translation became known as the “Latin Vulgate.” This is about the time the Catholic Church was founded. At this time they added what Protestants call "The Apocrypha," extra books not excepted as scripture by anyone but the Catholic Church.
By 500AD the Bible had been translated into over 500 languages. By 600AD, it was only available in the Latin Vulgate. The Catholic Church refused to allow the scripture to be available in any other language and burned every copy they could get their hands on. Those in possession of non-Latin scriptures were executed (generally by torture and burning).