Feel free to skip everything below if you want a nice quick short answer. The short answer is: "fides quaerens intellectum."
The longer (but likely flawed) answer?
I'd like to say that I sat down one day, learned every ancient language, studied every religious text of present day and antiquity, and after careful and thorough consideration concluded that the Hebrew and Christian Scriptures are indeed the Word of God...and unlike any other.
The more accurate answer is that I was taught as much year after year starting in 6th grade and that I began to question it in high school, but I didn't care enough or have sufficient discipline to act upon my questions and doubts. I eventually attended a Lutheran university as a physics and math major, and established heroes like Asimov, Hawking, Feynman and Sagan. But I was too undisciplined (and likely genetically lacking) to walk in the footsteps of my heroes. So, I studied history...and eventually theology. I liked theology, enjoyed the debates and talks, and craved to know more about spiritual matters. I was challenged to start reading the Bible daily by someone, so I did. I started by reading a chapter of Proverbs a day. It was amazing. Given that I didn't read much, the little that I did had ample room in my empty brain :). I was amazed to read Proverbs during the day and walk throughout the day seeing the wisdom of those words in my observations and interactions. I began to have similar experiences as I read other parts of the Hebrew and Christian Scriptures. The moral teaching and description of human nature made sense to me. The framework held up to my life experience...with a few exceptions. Eventually, I began to organize my thoughts and actions around the stories and events in the Scriptures. I craved not only knowledge, but intimacy with what I chose to believe as the source of that knowledge.
I then started reading parts of Christian classics and books related to the Scriptures in one way or another: books by people like Anselm, Augustine, Aquinas, Athanasius, Eusebius, Josephus, Tacitus, Suetonius, Pascal..to present day Christian apologists like: Montgomery, McDowell, Arndt, James Sire, Philip Johnson, C.S. Lewis, G.K Chesterton, Norman Geisler, Francis Schaeffer, etc. These (and a number of other authors) made a strong collective case that the Hebrew and Christian Scriptures are unique, even miraculous in nature...in essence the inspired Word of God. Somewhere along the line I came to view the internal evidence and the external explanations to be convincing. Of course, if I am honest, I really wanted to believe that the Scriptures were divinely inspired. It was definitely not an unbiased pursuit of truth.
Then one day I realized the ramifications of all of this. I started experiencing what George Herbert describes in his poem The Collar. I didn't want to believe in God or the truths of the Hebrew and Christian Scriptures, and at times I still don't. But, it was too late. I had read and studied too much to reject what was now altogether obvious to me, that the Hebrew and Christian Scriptures are indeed of divine origin in message. Unfortunately, I am still not a disciplined mind, and I suspect that my explanation of these matters is far too inadequate.