The novel The Outsiders more or less follows a pretty typical plot structure, which consists of an exposition (exposing characters and setting), a point of conflict, rising action, climax, falling action, and the resolution (or, a.k.a., the denouement); however, there also seem to be some minor climactic moments sprinkled here and there also.
In the beginning, or the exposition, we are introduced to the time period and some of the main characters, but we are also quickly shown one of the greater conflicts in the story - the clash between the greasers and the socs - when Ponyboy and some other greasers scuffle with some socs at the movie theater. There seems to be an attraction between Cherry Valance and Ponyboy, but readers understand the obstacles that this relationship faces.
This, of course, is an important conflict in the story - the age-old battle of the classes, the haves and the have-nots. Another possible struggle, though, is Ponyboy's internal struggle: is he truly a greaser like his family and friends? Is he somehow fighting against the limitations of his own culture?
The rising action, or growing tension, seems to center around the big "rumble" that's planned between the greasers and the socs, which leads to the climactic fight scene. Other climactic scenes, though, could be when Johnny and Ponyboy rescue the kids, when Johnny dies, and/or Dally's scene with the police.
The story ends brilliantly, with Ponyboy writing a paper for English class using the same lines that the beginning of the book uses. The resolution sort of leads us wondering where Ponyboy goes from here: does he fall into the predictable dismal life of a greaser, or can he follow Johnny's advice to "stay gold" and triumph over his environment?
For a more detailed summary of the plot, see the link below.