David prospered, Saul becomes jealous.
There are two sides to this story; the prosperous one and the jealous one. Let's look at the prosperous one first. It can certainly be said that God caused David to prosper, He caused all the right things to happen at the right time. David needs to be a willing recipient of God's blessing however. This willingness is partnered with patience, faithfulness and obedience. Really patience is inseparable with faithfulness and obedience - but it is key here.
David knew what Samuel had anointed him for, but was willing to be patient and let God work out the circumstances. Not only did he know that he would succeed Saul one day, but he also served Saul faithfully knowing this. I think it is clear that it wasn't David's motivation to supplant Saul, but to serve both him and God well.
Now on to Saul's jealousy, now who wouldn't be a bit jealous when you're king and your people are singing someone else's praises over you. You didn't really want to be king in the first place, but you accepted and you served and worked hard in it. Now someone else is getting a lot of the credit. Yes, I can understand maybe a moment of jealousy. But, this is happening in more than one place, it was happening in all the cities of Israel. So it was becoming a constant and nagging pain.
After having identified with Saul about the issues he faced, really I need to ask. What was the proper response? Maybe as the leader be focusing less on praising one person over the other and focus more on praising the One Who really brought the victory. Saul knew that God wasn't going to let his dynasty succeed, but as leader of the nation he could have been more of a Moses going out strong and less of a sore loser. Even though Moses sinned, he remained faithful and was remembered as godly. Saul isn't remembered that way.