It would seem that good priests do not beget good priests. Samuel's sons are as bad as Eli's, accepting bribes and perverting judgement, whatever that means. The people come to Samuel and demand a king. God is offended, seeing it as a personal rejection of all he's done for him. Samuel informs the people that if they appoint a king, he'll essentially be a feudal lord: work will be assigned and he'll claim the best crops as a tribute. Not unlike when Joseph controlled capital and labour back in Genesis, no? But of course he was righteous and for some reason here it isn't, so it's bad.
But the people ignore him and want a king anyway, so god says go ahead, but don't come crying to him.
Saul is introduced. He's tall and good-looking, which according to Jerry Falwell is the first qualification of a good king. So, as the least horsey member of the British royal family, Zara Phillips is the best qualified to rule?
Our first meeting of Saul is less than auspicious. He has lost his father's donkeys. He gets bored of looking for them, but he's heard that Samuel is in town and decides he's the person to ask about some lost animals. He decides to bring him a quarter of a shekel. They arrive in the city just in time for a major sacrifice.
Now, before all this, god had told Samuel that he would meet the king that day, and when Saul appears, god points him out as his anointed choice. Saul asks Samuel where the prophet is, and Samuel says he's it, and invites him for dinner and a psychic reading the next day. He also says not to worry about the donkeys, and that Saul has been chosen as king.
Saul is reluctant, pointing out he's an unimportant member of the least powerful tribe, but Samuel will have none of it, seating him at the head of the table and giving him the choicest piece of meat. The next day, they go to the top of the house, and Samuel says he's going to show Saul god. What do you want to bet 'god' lives in his pants?
Nope, it wasn't a trousers-snake, it was even better! Samuel pours oil over his head, then sends him towards the border, where he'll encounter two men who will have a message: the donkeys are safe. He's to keep going to the plain of Tabor, where he'll find three men, one carrying 3 goats, another with 3 loaves of bread, and the last with a bottle of wine. They'll salute him and give him bread. Next, he'll travel on towards the Philistines, where he'll meet some prophets carrying stuff. They'll be prophesying, and then he'll be taken with the spirit of the lord and he'll start prophesying, too. After a week, Samuel will come along to offer burnt sacrifices. Saul leaves and lo and behold, everything happens as predicted. The people see Saul and coin a new proverb Is Saul also among the prophets (v. 12) which I was not familiar with, but which apparently is used when somebody known for doing bad suddenly starts doing good.
Saul eventually comes down from his religious frenzy and sees some of his uncles, who ask about the damned donkeys. He repeats what Samuel said about them, but not the rest of the story.
Meanwhile, Samuel calls the people to Mizpeh and tells them he's going to select the king by lots, and of course it comes out Saul. But Saul has disappeared! Only god knows where he is, hidden among the 'stuff', which might mean baggage, or at home, or goods, depending which translation you prefer. Saul is hauled before the people, who like him because he's tall. They deserve what they get, really. Then Samuel reads out the laws of the land and writes them down in a book. Then everybody goes home. The people of Belial don't want Saul as their king.