This is one of the most important questions in theology.  If the Bible is not reliable, then all we have is opinion.  If it is reliable, then we have truth from God.

Method 1

Show that there is a complex pattern in the text of all the books of the Bible.  The books of the Bible were written by a number of different authors.  If this pattern is the same in all the different books, and if it's more complex than even the most gifted authors could write, then if it didn't come from God, where else could if have come from? [ See Numeric Structure ]  An interesting reference is:  The Original CODE in the BIBLE by Del Washburn, 251 pages, Madison Books Lanham, New York – Oxford, ISBN # 1-56833-115-0

Method 2

There are a lot of prophecies, i.e., predictions, in the Old Testament.  Show that they come true in the New Testament or have not had time to happen yet.  If God originated the Bible and guided the people who wrote and assembled it, then all the predictions will be accurate.

Method 3

Show that there are no errors or contradictions in the text, and show that the original text has been accurately preserved.  If what we have now matches the oldest copies we can find, that shows that no editorial changes have been made.  If God wrote it, it won't have any errors in the original text.

People will point to things they think are contradictions, but keep looking, there's always a good explanation.  There are translation difficulties, and issues about how well small bits have been preserved, but the evidence in support of the Bible being error free is substantial. See Oxford Scholars Skit.