If you mean the Protestant Bible, the story goes roughly like this. The "Old Testament", or Hebrew Scriptures, over a period of about one millenium, between the 16th and 5th centuries, though the exact date for many is unknown. Many of them were written in response to the Babylonian exile of the 6th century- the current Hebrew Script was developed at that time, and the many oral traditions from which the books of history were written from were compiled, perhaps for fear that knowledge would be lost in the event of later cataclysms. Many of the books of prophecy also relate to that event. In 450 BC, the Jewish Scriptures were arranged and codified by a council of Rabbis, who declared the Hebrew Scriptures to be the sacred and inspired authority of Elohim. These are also referred to as the Tanakh, an abbreviation of the three sections into which they are organized. This order was not maintained when the Scriptures were translated into Greek in 200 BC, a volume known as the Septuagint, named for the seventy men employed in the translation. Most Christian Bibles maintain the order invented for the Septuagint, and New Testament authors tended to quote this version rather than the original Hebrew, save for (probably) Jesus himself.
Beginning about 20 years after Jesus' death, a number of Gospels (literally "good news"; gospel was not necessarily a book, but in literature it usually referred to an account of Jesus' life, like the canonical gospels, or one of his teachings, such as the gospels of Thomas or Peter) and books of the apostle's acts began to surface throughout the areas of Israel, Syria, and Asia minor. Most purported to have been written under the influence of Christ, either in person while he lived or through revelation after his death. Such books were kept and revered mostly by individual communities, but copies of well-known gospels began to spread throughout Europe. By 397 AD, so many books were in circulation, many supporting movements that the primary body of the church considered heretical and dangerous, that a council was convened to decide once and for all which books should be considered canon, and which ones should not. This was the aforementioned Synod of Carthage. Much of the New Testament had been established by consensus by this point, but the Synod of Carthage both codified the most popular arrangement and officially included the Septuagint into the realm of canon. Hebrews, James, II Peter, II and III John, and Revelation are the books that were the most controversial at the time - even in the Medieval Period, many of these had a less important position, and Martin Luther is well known for his desire to decanonize Revelation and James completely (on the grounds that they do not directly mention the Gospel). In 1546, the Roman Catholic Church officially adopted a dogmatic position on the canon, at the Council of Trent. Exactly which books are included in the Old Testament varies widely between denominations, but the new Testament is more or less agreed upon (in content, if not order). The only exceptions to this are in the scholarly realm where many books are still being considered for inclusion or exclusion from consideration based on historical or linguistic evidences.
Later changes of importance to you would include the collection of the complete Bible as a single book, in 1384, the translation of the Bible into English, first accomplished in 1526 AD, and the addition of numbered verses to English language Bibles in 1560. The KJV originally held 80 books, including those known as the Apocrypha. Several of these were officially dropped in 1885 with the publishing of the English Revised Version, leaving the Bible as a unified book containing the 66 books most familiar to you.
I've glossed over quite a lot, and I would encourage you to research these matters yourself, and draw your own conclusions. No doubt, someone will be along presently to correct the various mistakes I've made, but I figured you would appreciate a full summary, so I was going from memory. There are many, wonderful resources out there for those curious about the Bibles origins. I don't actually believe that the Bible is the Word of God, myself- I believe that it contains the Word of God, which is Christ, but that it does so imperfectly. When there are hundreds of translations running around, each claiming absolute authority and each serving a local societal or political need, I think it is unwise to ascribe inerrancy to any one version. Rather, I read all of them with interest and devotion, and ask for the assistance of the Holy Spirit in teaching me which things are important, and which are less so.