Most good stories start with a fundamental list of ingredients: the initial situation, conflict, complication, climax, suspense, denouement, and conclusion. Great writers sometimes shake up the recipe and add some spice.
Exposition
Don't Try This At the Library
Artemis finds a fairy and blackmails her for a copy of her Book, which he then translates and uses to plan his whole money-making scheme. This is the whole reason the rest of the novel is even possible. Without the fairy Bible that gives away all their secrets, Artemis would have been mind-wiped in the first few chapters and the rest would probably be full of jokes about another Irish Mud Boy who thought he could get his hands on the gold at the end of the rainbow.
Rising Action
Kid... er... Elf-napping
After successfully elfnapping Holly, Artemis finds out she's actually Captain Holly Short of the LEPrecon unit, and she's got a whole bunch of fairies coming to get her. Also, she's super dangerous when she has her magical powers. Also also, her friends are bringing a troll. And a time-stopping device. And a very red-faced, old-school Commander. If he had grabbed any other fairy, Artemis might have gotten away with it, but nabbing Holly ensures that Artemis's plans will need to be changed and made up on the run.
Climax
The Rinse Cycle
There's a fight going on in Haven and some fairies reveal they're a little too comfortable with ending non-fairy lives when they decide to "blue rinse" Fowl Manor with a biological bomb that will kill every living thing... unless Artemis can escape, which he claims he can.
At this point, everything could go very wrong for Artemis. It's one thing to be smarter than everyone else, but it's a whole other thing to use those smarts to trick his best friends into taking sleeping pills while letting them believe they might be about to die. Artemis certainly believes his plan will work, but then again... how often does Artemis doubt himself?
Falling Action
Fairies Make Terrible House Guests
After the bio-bomb is detonated, the fairies sweep in to clean up any mess (a.k.a. dead bodies) and take back their ransom gold, only to make a new mess by hurling all over the floor when they try to enter the house. It turns out that Artemis is still alive and they can't enter without permission, which pretty much means that the action is done in the book. The fairy rules say the game is over.
Resolution
Fairy or Fowl
Artemis, by doing nothing except living through all the fairy nonsense, wins the right to keep the gold and be left alone. We realize at this point, however, that he gave back half the gold in exchange for Holly healing his mother's mind. We know Holly's not finished with Artemis Fowl II yet (making an enemy out of her wasn't a great plan) and there's a pretty obvious sequel setup, but Artemis is filthy rich once more, which puts the closing touches on this adventure (since his whole point was to regain his family's ridiculous wealth through this adventure).