Conflict in a story begins with some kind of trigger or event which sets the plot in motion. Before then, the story may contain exposition or foreshadowing to set up the plot, but the instigating force is the first actual moment of conflict in the story proper. For example, the triggering event in a mystery may be a murder which sets the detective on the trail of the killer, while the triggering event in a romance may be the central couple’s first meeting.
From the triggering force, conflict in literature slowly escalates through the rising action. The protagonist or protagonists faces an increasing series of obstacles standing between them and their goals. Depending on the specific type of conflict, these obstacles could be physical -- such as a villain sending minions to stop him -- social, such as a revolt or uprising in the city where the protagonist lives, or mental -- such as the protagonist wrestling with his own fears and doubts.
The climax is the ultimate point of conflict in the story: the period where the protagonist either overcomes the forces arrayed against him or her, or succumbs to them. Usually, the entire work builds up to this moment, as the conflict reaches its crescendo and the question of its resolution is finally answered. Examples can include a final duel between the hero and the villain, a detective uncovering and arresting a murderer, or a romantic couple reuniting after countless efforts to keep them apart.
With the climax resolved, there may be a few residual elements of conflict before the story formally ends. This usually entails “wrapping up” any remaining plot threads. It could include such elements as the trial of the murderer in a mystery or the wedding of the central couple in a romance.