On his first day of high school, Kyon notices Haruhi-- how can he not? She introduces herself as someone completely uninterested in "normal" humans, but hoping to meet any aliens, time travelers, or espers at the school.
He establishes a tentative friendship with her and unintentionally gives her the idea of starting a new school club, which she does. She calls it the SOS Brigade, and its stated goal is to find aliens, time travelers, and espers.
Haruhi drags others into the club, starting with Yuki Nagato (who simply came with the room Haruhi claimed for her own, which was formerly the Literature Club room). Next comes MIkuru Asahina, a cute second-year student Haruhi enlists to act as a "mascot" for the club. They are later joined by Itsuki Koizumi, a "mysterious" transfer student.
As the year wears on, each of these three comes to Kyon and informs him that they are one of the things Haruhi seeks: Yuki is an alien robot, Mikuru is a time traveler from the future, and Koizumi is an esper. Each also posits that Haruhi has the unique ability to alter reality as she sees fit; she is, in fact, the reason they exist and are near her. But she is completely unaware of this ability...and while the three (and the groups they represent) don't see eye-to-eye on everything, they DO agree that she should remain in the dark.
Thus embarks Kyon's journey to prevent Haruhi from destroying the world!