How can you believe the New Testament since it claims supernatural events?

This is an unfounded objection because: it is only part of the story. It is true that the bible claims supernatural events, but it then backs up those claims with fulfilled prophecy. Great examples of these prophecies are found in Isaiah chapter 53, and Psalms 22 where the writer predicted the extremely specific conditions of the execution of Christ hundreds of years before it happened.
By divinely interpreting a dream the Prophet Daniel predicted the rise and fall of four world empires.

In the New Testament Jesus predicted the fall of Jerusalem in 70AD forty years before it happened. In Matthew 24 Jesus not only predicted the fall of the nation of Israel but also her reestablishment which took place in 1948. This was considered an impossibility for centuries, until it happened. These prophecies were thought to be figurative for thousands of years. in 1967 Jerusalem was recaptured by the nation of Israel. All of these fulfilled prophecies are evidence toward the reliability of scripture.