To understand the summary of the text, it is important to have a basic understanding of the major characters:
Protagonist: Percy Jackson
Friend of Protagonist: Grover
Love Interest: Annabeth Chase
Antagonist: Luke Castellan
Various Gods: Zeus (earth), Poseidon (sea), Hades (death), Ares (war), Athena (wisdom)
I'll map the summary for you using Freytag's Narrative Structure:
Exposition: Percy Jackson is introduced as a troubled young man with learning disabilities who does not fit in. He is on a class field trip.
Inciting Incident: He is attacked by ancient Greek monsters on the field trip and fights them off with a sword, but then no one else claims to remember this incident.
Rising Action: That summer, Percy and his mother are attacked by another monster, at which point Percy stumbles upon a camp for demigods, or children whose parents are one god, one human. It is revealed that Percy is the son of Poseidon, which should be impossible since Poseidon and his two brothers (Zeus and Hades) have agreed to father no more children. Percy and two friends go on a mission to recover a missing lightning bolt in an attempt to stop all-out war among the gods (due to the lightning bolt and Percy's birth). He battles many monsters over the course of the journey.
Climax: In L.A., Percy discovers that Ares has the bolt and fights him for it. Percy succeeds.
Falling Action: Percy solves issues that have arisen over the course of the journey with several gods, including the return of his own mother to earth.
Resolution: Percy returns the bolt to Zeus, who in turn allows Percy to live. Percy returns to camp a hero.
Denouement: Luke turns on Percy, revealing the fact that Titans, the mythical parents of the gods, have been behind the whole ordeal. Percy refuses to join Luke, who attacks Percy. After his recovery, Percy decides to return to his mother, and the novel ends.