Explain Percy's quest in detail.
Like any good adventure myth, Percy Jackson and the Olympians: The Lightning Thief has a classic hero's journey plot. Percy, the hero of the story and son of the Greek god Poseidon, is called to go on a quest.
Every "hero's journey" type story, from the Holy Gospels to Star Wars, vaguely follows the same set of steps. Some critics say there are 17 steps, others say 12, others say 3 – no matter how much in detail they're divided, they still follow roughly the same plot. (For more on this, check out the links to a video and written explanation below!) Let's see how these look for Percy Jackson:
The Ordinary World: When we meet Percy, he is a regular kid with regular problems: he struggles with school, he loves his mom and hates his step-dad, he has a best friend. This is the part of the story where we see what "normal" looks like for the hero, before the adventure starts.
The Call to Adventure: This is the moment when we know things are changing for the hero. At a school field trip, Percy's teacher Mrs. Dodds turns into a winged monster and attacks him. His favorite teacher, Mr. Brunner, runs in at the last second, throws Percy a sword, and disappears. Percy kills the monster, which vanishes. When he's back outside, it's as if nothing has happened. No one recalls a "Mrs. Dodds" and there is a new teacher in her place.
This is all really confusing for awhile, and Percy grows increasingly suspicious. But the mystery is not cleared up until he and his mother are at their beach house, when Percy's best friend Grover shows up unexpectedly. Grover and Percy's mother give him advice about the monster that has apparently discovered Percy's whereabouts. After a fight with the monster (a minotaur), Percy mom has disappeared (and he assumes she's dead) and Percy has defeated the monster.
Crossing the Threshold (and some Meeting with the Mentor): A dejected Grover, disappointed that he hasn't protected Percy better, leads Percy to Camp Half-Blood, which turns out to be a camp for demi-gods (the children of gods and mortals). Now Percy is completely immersed in the world of the gods. Mr. Brunner is there, in his true form, a half-man, half-stallion called Chiron. Grover, actually a satyr is there as well, along with many other creatures out of Greek mythology.
The Road of Trials (Enemies and Allies): Like all great heroes, Percy is reluctant for a quest at first. Upon learning that his father, who he now knows is Poseidon, is in an epic fight with Zeus and Hades over Zeus's missing "master bolt" and that now that he is clearly Poseidon's son, everything will think he took it, Percy is naturally overwhelmed. Still, like all heroes, he ultimately goes, spurred by the knowledge that his mother is alive, but kidnapped by Hades.
Now Percy, Grover, and Annabeth (daughter of Athena) are off, to go to Los Angeles (entry to the Underworld) and try to find and recover the master bolt. Along the way, they meet minor enemies, like one would in a video games (because lots of these are hero's journeys too!) Mrs. Dodds is back, with 2 friends – they are the 3 Furies sent from Hades, and the trio has to fight them and eventually blow up the bus the trio is riding on to stop their attack.
The trio escapes into the woods, but it's not long before they find themselves in a suspicious situation again. They've found a burger joint and are so engrossed in the greasy food that they fail to realize that the proprietress "Aunty Em" is none other than Medusa. Again, they fight their way out just in the nick of time.
The third battle, Percy is alone, at the top of the St. Louis Arch, with the Mother of Monsters Echidna and her son, the Chimera. This is a battle Percy doesn't win, but he does escape, by diving off the Arch into the Mississippi River and praying his father will save him. At this point, Percy hears from an ally as well. A water spirit, sent by his father, tells him to have hope, that all is not lost.
The road of trials continues: the trio is side-tracked by a quest from Ares to retrieve his shield and then accidentally spend 5 days in a mysterious time-looped casino. In Los Angeles, Percy gets another message from Poseidon, and some magic pearls. After another run-in with another Greek monster, the trio finds the entrance to the Underworld.
The Ordeal/The Descent into the Underworld (literally): This is the Big Boss of the Hero's Journey. Up until now, the trio has assumed that big boss would be Hades. When they do meet him, though, they discover that the theft of the master bolt was done by another figure, one not even involved in Zeus, Hades, and Poseidon's bickering. Percy figures it out and escapes Hades to confront the real villain: Ares, god of war. After fighting him, they had retrieved not on the master bolt, but the helm of darkness, which they return to Hades into to release Percy's hostage mother.
Reward: Percy travels to Mount Olympus to return the master bolt in person and have a heart-to-heart with his father. His father tells him he's sent a present to Percy's house. When Percy returns home (and reunites with his mother), he discovers the present is Medusa's head, which he gives to his mom as a way to escape Smelly Gabe, if she ever chooses to use it (she does).
Master of Two Worlds: Percy spends the rest of the summer at Camp Half-Blood. He feels like he's finally found a real family and is pleased to hear that his mom turned Gabe into a sculpture and used the money to make a new life for herself, and him, if he wants it.
*The Call to Action for Next Time!* - At the second climax of the story, Luke, a figure at Camp Half-Blood reveals he was behind all the theft of godly artifacts. He tries to poison Percy and escapes, setting up the perfect quest for next time...