Daniel was a man full of wisdom, and there are so many lessons to take from these chapters that it's hard to narrow it down to one.  However, there is one characteristic about Daniel's life that is worth noting here: he recognized God's sovereignty.  It's just a simple comment in Daniel 2:21, but it is indicative of how Daniel lived his life.  He recognized that God is in charge, and that God places people in authority.  God allowed the kings who ruled over Daniel to have their places of authority, and it was his prerogative for when they would be removed from power.  In light of this knowledge, Daniel lived in submission to the authority so long as it didn't violate his submission to the Lord.  The same should be true for us.  God allows others to be in authority over us, and we need to submit to them if for no other reason than because we know He put them there.  God is the One who appoints kings, and He is the One who can remove them, too.  No one has authority but that it was given him from God, and no one loses authority but that God takes it away.