There are multiple ways. Ultimately, it does boil down to having Christ as savior in your life. After all, many of the things state in the Bible seem outlandish unless you've "bought into the system." That doesn't mean those things are wrong - after all, that's how it is with every belief - just that until our wrong presuppositions change to the right ones, it's going to be hard to accept certain claims. However, I would point to a few things that point in the direction and lend substance to the claim of a reliable and inspired Bible (but none of these prove it):
1) Historical accurate - we know that a good many of the events claimed in the Bible actually happened and even its references to external history match what we know to have existed in history.
2) Test of time/persecution - no other book has been suppressed as much as the Bible has been suppressed. It has stood the test of time in many ways. For instance, if we take the various manuscripts of the Bible (from 50AD to 400AD), compare the differences and then compare them to the major English translations, they are 95-97% similar and accurate. The small differences are either on non-translatable words from Greek into English or on numbers and grammar usage. Throughout all of this, it has withstood the test of time.
3) Self-authenticating - it claims to be an authority and if applied as an authority, it "works." I don't want you to apply a pragmatic test to it, that seems too much like an informercial to me. "Try it for 30 days and if you don't like it, you'll get a full refund!" Honestly, sometimes it doesn't "work" for non-believers because there is no Holy Spirit within the person to actualize the teachings of the Scripture in a person's life. What you can do, however, is see what it has done for people in the past who have claimed Christianity. You can see the authority it has taken over people's lives and how this has led to a "better" life for them (I put better in quotations because I really mean happier, not better as in the American understanding of the word). You said elsewhere that you can live by the principles and morals of any religious book and have a good life - and I agree, you can. This is why I'm against the pragmatic test of the Bible; such a test authenticates any religious work. However, the unique aspect of such biblical authentication is that it fits within the system and doesn't contradict anything else within the system.
4) It explains the whole of existence - I think of a Christian philosopher who holds a great influence on my life and the story of his conversion. He began reading the Greek philosophers while he was lost. After finding that they had many questions, he began to read the Bible after someone witnessed to him. He read the Bible from Genesis to Revelation. He was shocked - the Bible answered all the questions the Greeks had. You don't have to accept the answer the Bible has, but it provides answers for all the major questions in life in a coherent fashion.
5) It's coherent - as I stated above, the Bible is a coherent answer to the philosophical questions in life. It is noncontradictory and presents a logical system of belief that doesn't contradict itself (like the redundancy?). You don't have to believe the answers, but you can be sure of two things: (1) The Bible will give answers that aren't far-fetched and (2) the answers don't contradict other beliefs and aren't non-sequitur with the system; every answer logically flows from another aspect in Christianity, due to its coherency.
I hope that helps. If you don't understand something I said, feel free to ask me to clarify. Again, none of these prove that the Bible is inspired or reliable, but it does give quite a bit of credence to the claim, more credence than any other holy book written.