God tells Samuel to quit moping over Saul and hie himself to Bethlehem so he can meet Jesse, one of whose sons will be the next king. That rather makes it into an errand instead of a treasure hunt, doesn't it? But that's not the end of his micromanaging: Samuel is to bring a heifer and ask Jesse to sacrifice with him. God will reveal the next king during the sacrifice.
So Samuel goes along and invites the town to his barbecue. He spots the first of Jesse's sons, who is tall and handsome, and immediately thinks that's his guy, because it worked so well with Saul. But god rebukes him for going for looks over substance. As in Cinderella, god rejects seven of Jesse's sons, until Samuel, at the end of his wits, asks if those are all his kids. Jesse says no, the youngest is shepherding. Samuel asks to meet him.
So much for inner beauty being the most important thing: David is ruddy, and withal of a beautiful countenance, and goodly to look to (v. 12). The spirit of the lord then leaves Saul, to be replaced by an evil spirit of the lord. Now, how it is possible that a god that is entirely good could infect someone with an evil spirit is an extremely tricky theological task, so here's Jerry Falwell's attempt at explanation: The evil spirit is said to come from God because, although God is neither the author of evil nor tempts any man with evil, all forces, natural and supernatural, are under His ultimate control. Wow. Stunning. God did it, but isn't responsible, because he isn't evil, even though he controls everything. The end. Shut up and pray. I really wish there was a cheaper, shorter version of the Anchor Bible not written by crazies.
Saul's servants notice the evil spirit, and I can't help but picture Linda Blair here, and suggest music therapy. And who is the musician? Why, David! Who is again described as comely (v. 18). Saul is instantly smitten, and even better, David's harp playing calms his evil spirit.