In the first book of Samuel, the people were still led by judges or prophets.
Samuel, as a boy, was called by God to become a prophet. God called Samuel's name, waking him several times from his sleep. Samuel obeyed God and became a prophet.
Later, the Israelite people clamor for a king. Samuel reminded them that God is king, but, if it's a king they wanted, a king they'd get so long as the people remember God is the true king.
Samuel anointed a King, Saul. Saul leads the people for several years, until his "greatness" goes to his head.
Saul disobeyed God and took it upon himself to make a burnt offering. Only the prophet was supposed to make the offering.
After Saul disobeyed, he was no longer in Gods' favor. Saul realized his mistake, but his pride and arrogance kept him out of the Lords' favor and ultimately drove him to madness.
While this was all taking place, a little boy named David was becoming very popular with the people. David, through faith, killed a giant Philistine, Goliath, with a sling and a stone. Goliath and the Philistines were attacking the Israelites.
David was also Jonathans' best friend. Jonathan was Sauls' son. David also sang and played the harp for Saul to sooth his nerves.
David grew up and started to fight battles on his own, as he defended the Israelites against the Philistines. David tallied more victories than Saul. Saul became jealous and tried to kill David. David didn't understand Sauls' madness. Saul finally killed himself.