An important manuscript (ancient copy of the Bible) connected with your Bible at home is called Codex Sinaiticus. It is described as "a manuscript of the Christian Bible written in the middle of the fourth century" that is "the earliest complete copy of the Christian New Testament."
A historical occasion is occurring as it is being scanned and released to the public progressively over the next year or so...want to see it? Check it out HERE!
If you want a short explanation for the documentary evidence of the Bible, chapter three of The Case for Christ by Lee Strobel is a great place to start.
If you want a more in-depth explanation, to include references, photos, and a detailed history of discoveries, you should check out Journey from Texts to Translations: The Origin and Development of the Bible by Paul Wegner.
Several great pamphlets are also available (from Rose Publishing, an awesome producer of Church-quality charts and pamphlets) called "The Bible Translations Comparison," "How We Got the Bible," and "Why Trust the Bible?"