A boy named Percy Jackson is on a school trip when his math teacher turns into a monster and tries to kill him. He saves himself when another teacher throws him a ballpoint pen that turns into a sword. Whereupon everyone acts as if that teacher had never existed.
He hears that teacher talking to another student, Grover, about the danger Percy is in. And then, when he returns home, he find his mother thinks he's in danger, and she's to blame for keeping him with her. But when they set out, they are attacked by a Minotaur. His mother vanishes, and Percy barely manages to escape to a summer camp alive. There, he finds that the teacher with the pen is Chiron, Grover is a satyr, and he himself is a demigod -- of an unknown father.
He meets people, learns some swordplay, helps with capture the flag -- but problems are piling up. When he learns his father, it shows that a god has broken an oath. And there has been conflict among the gods because of a theft. Finally, a monster in the camp leads Chiron to send Percy to consult the Oracle and send him off on a quest to stop this, with Grover and with Annabeth, Athena's daughter. (No, there is no explanation of how Athena has children in the book, though there will be one later in the series.)
Whereupon the tale takes on a trip across the United States. It involves a car wash, a train, a zebra, taunting a god into a fight, playing with Cerebus with a big rubber ball, a mattress place, whether Echinda is an ant-eater, and more. Adventures all over the place.