The fiery furnace incident is thought to have occurred in the 18th year of Nebuchadnezzar's reign, after Daniel and his three friends had been in Babylon about 20 years.
Just as God had revealed to Daniel the dream of Nebuchadnezzar, and its interpretation, years before, He now puts into the hearts of these three men the firm determination to be true to Him. He then goes with them into the fire, not only to honor their faith, but to demonstrate before the assembled dignitaries the power of the God of Jerusalem over the boasted gods of Babylon. Thus a second time God manifested Himself in the palace of the mighty empire, and a second time the mighty Nebuchadnezzar bowed before God, and proclaimed Him to be the true God to the utmost bounds of his empire.
Chapter 4 is actually an official Babylonian document, written by King Nebuchadnezzar. It is the story of his conversion, and what a story it is! Keep in mind that it was written seven years after the experience took place, so verses 1, 2, 3, and 37 are Nebuchadnezzar's public testimony of what God did to him and for him.
In chapter 4 we see the dream received (verses 4-18); the dream revealed (verses 19-27); and the dream realized (verses 28-36).