Chronologically episode 1.  It's the first day of school and Haruhi Suzumiya sits just behind Kyon.  When she introduces herself, she states that she has no interest in normal human beings but instead wants to associate with aliens, time travellers and espers.  Kyon notices some eccentricities about her: she joins all of the clubs in school but never stays and she never says no to a date but never has a boyfriend more than a week.  Kyon eventually gets her to talk to him by noticing that she changes her hair style everyday.  When he, in a roundabout way, suggests that she form her own club, that's exactly what he does, with Kyon as the first member.  The second member is rounded up shortly after and her name is Mikuru Asahina.  She's chosen by Haruhi because she's cute and there's always a cute girl involved in any mysterious happenings.