As writers we have the power to alternate the lineal order of events to create intrigue, to generate expectations that hook the reader, or simply to delay that key scene that will serve as climax in our story. For their way to begin narration, non-lineal organization of plot can be divided in two groups:
There are books that begin with a fact that takes place in the middle of the story, with the characters already in the middle of the conflict, without previous explanations, nor introductions or presentations. This technique is known as In Medias Res, and it generates expectation and interrogation in the reader, who will have no more choice than to keep reading to know the characters and the development of the conflict. To tell the previous events, we shall go back in time with retrospections or flashbacks. The In Medias Res technique is really old (Homer used it in The Odyssey and The Iliad), but it is very active nowadays due to our audiovisual culture and its tendency to “start really up”.
The second way to begin narrations in non-lineal plots, is the technique called in extremis, in which the first scene we tell is the last one in the story. With this we intend to make the reader wonder which has been the path that led the character to this point. After this beginning, the facts in our story can be ordered in a chronological way from the beginning to the scene that opened the novel, which is called circular structure or racconto. On the contrary, if we decide to tell the facts in a non-lineal way, ordering them by their degree of intensity or importance, we will be using a homeric structure.
When we have structured our story in a synopsis, there is another step (there are several other steps actually) that we will need to complete in order to have our argument: incorporating sub-plots. As you may have guessed, sub-plots are practically the same as the main plot, but with a secondary importance and a usually shorter length.