Here's the backstory: The Fowl family is a family in the Godfather Irish mafia kind of sense, and they're an extremely dangerous family at that. After Artemis Fowl I (the main character's father) disappears under mysterious circumstances though, the family becomes slightly less scary and slightly less rich—but worry not, Artemis Fowl II, a twelve-year-old genius with a talent for crime, has a plan to change all that.
Through a combination of Internet research and wild rumor, Artemis figures out that all of the children's stories and legends of magical creatures in different cultures refer to the same group of fairy folk (the People) who have been living underground, away from human interference.
What's more, each fairy has a Book that contains all of their magical secrets in one convenient location. Artemis, of course, has simple tastes—all he really wants is the fairies' gold. So he blackmails a drunken fairy into giving him her Book, photographs the pages, translates the Gnommish language it's written in, and realizes the fairy gold in the legends is actually just a ransom fund for kidnapped People. Ah-ha.
Step Two is pretty obvious, though kidnapping a fairy is harder than it sounds. Artemis gets more than he bargains for when he and his bodyguard, Butler, kidnap Captain Holly Short, a hotshot LEPrecon officer (even though he manages to nab her when her magical powers are at an all-time low). Holly's boss, Julius Root, goes on a rescue mission, Holly gets her powers back, and Mulch Diggums—the flatulent dwarf—is sent in to find out where Fowl is getting his info. Oh, and some fairies think stopping time and releasing a troll in Artemis's house are great ideas.
Long story short, Artemis's plan goes crazy, Butler is taken out by a troll and almost dies, Holly heals him and makes everyone question who the bad guys really are, and the fairies decide to just give it up and "blue rinse" the house, killing every living thing inside. In classic Artemis (Artemisian?) fashion though, he figures out how to do what no one has ever done before, and escapes the time-bubble and the biological bomb—which, by a weird twist of fate, means the fairy rules declare him the winner and he keeps the gold.