This is an upper middle grade fantasy, a la Harry Potter except the "school" is for half-bloods - children with one parent who is a Greek God, instead of a school for wizards. My book the Valley of the Unicorns is middle grade level, so I am really studying the craft of this best-seller. I am also eager to read the next book in the series.
What I learned from the Lightning Thief:
Each chapter is its own little mini-adventure. Some monster or bully or god must be faced or fought, some kind of race or challenge won, some friend or family member saved from terrible disaster. Each chapter has a funny title, such as "I Accidentally Vaporize My Pre-Algebra Teacher", and "We Visit the Garden Gnome Emporium."
Coincidently, just noticed an article, Tips on Middle Grade fiction: What Kids Love at the excellent blog, Guide to Literary Agents. I'm glad to see that my observations on the Lightning Thief line up well with the article's.
Humor is rampant, and even if it's not even remotely realistic, it's still fun. For instance:
See, bad things happen to me on field trips. Like at my fifth-grade school, when we went to the Saratoga battlefield, I had this accident with a Revolutionary War cannon. I wasn't aiming for the school bus, but of course I got expelled anyway. And before that, at my fourth-grade school, when we took a behind-the-scenes tour of the Marine World shark pool, I sort of hit the wrong lever on the catwalk and our class took and unplanned swim. And the time before that... well, you get the idea.
Not in every chapter, but in many of them, the author takes a strange, fantastical scene - such as a scene of the dead filing into Hades - and puts a familiar, funny twist on it. For instance:
There were three separate entrances under one huge black archway that said YOU ARE NOW ENTERING EREBUS. Each entrance had a pass-through metal detector with security cameras mounted on top... the dead queued up in three lines, two marked ATTENDANT ON DUTY, and one marked EZ DEATH. The EZ DEATH line was moving right along. The other two were crawling.
Summary: you can get away with exaggerating humor for midde-graders. You have to have constant adventure/action. You have to link fantasy with real-world things.