Supernatural Origin of the Bible

The most obvious answer is that the Bible itself claims to be the Word of God, delivered to his people through various covenant representatives such as Moses and the Prophets. These men stated explicitly that the messages they delivered were from God (through phrases such as "the Word of the Lord," "Thus says the Lord," Moses' account of speaking with God on the mountain, etc.). The miracles and wonders that sometimes accompanied their ministries also attested to the truth of their claims, such as the crossing of the Red Sea in Moses' day, or Paul's raising of Eutychus from the dead. These facts should give Christians great encouragement that the Bible we have is the very Word of God.

But frequently when people ask this kind of question, they aren't really willing to take the Bible's word for things. Often they are opponents of Christianity who want to see some real proof that the Bible is supernatural, such as verifiable fulfillment of prophecy, or a working formula that can be repeated by anyone to reproduce an answer to prayer. The greatest example of such proof that I can think of is Jesus Christ himself. In the Old Testament, God told his people that he would send his Messiah, his redeemer who would destroy Israel's enemies and bring great blessing to Israel. And when Jesus actually came, he began to meet these very expectations. Of course, he hasn't finished meeting them yet, but the fact that the church has grown so much, and that it includes so many Gentiles, and that persecution actually seems to make it stronger -- these things all indicate that Jesus was who he said he was. And if he was who he said he was, then we can find all sorts of fulfilled Scripture in his person and ministry. This, in turn, indicates that the prophecies were true and that the Bible is supernatural.