In Chapter Nine, Tom and Nick run into each other in late October on Fifth Avenue. This is after the events of the summer that culminated in Wilson murdering Gatsby and then committing suicide. In the rising action, Nick sees Tom, observes his aggressive movements, and slows down so he won't overtake him. Tom, however, glimpses Nick's reflection in a shop window and comes toward him, his hand held out. Nick refuses to shake hands, saying "you know what I think of you." Tom tells him Nick is crazy, and Nick asks him what he said to Wilson that caused Wilson to shoot Gatsby.
In the climax of the scene, Tom tells Nick that Wilson arrived at his door with a revolver and demanded to know who ran over Myrtle. Tom told Wilson it was Gatsby. Tom speaks defensively, implying he feared Wilson would shoot him and saying Gatsby had it coming for running Myrtle over like "a dog."
In the falling action, Nick realizes that Tom believes this version of the story; he doesn't know Daisy was the one driving the car. Nick understands there is nothing he can say, as he won't expose Daisy by telling Tom that his wife killed his lover. Nick recognizes, too, that Tom feels he was victimized by events and believes he was justified in sending Wilson after Gatsby. Tom talks about how sad he felt after Myrtle's death, crying over the box of dog biscuits he found in her apartment.
As Nick comes to have some sympathy for Tom, he ruminates on Tom and Daisy, deciding, in a famous passage, that they were "careless people... they smashed up things and creatures and then retreated back into their money..." At this point, as Nick's anger fades, although he never actually comes to like Tom. Nick decides Tom is childlike and shakes his hand, deciding it would be silly not to shake hands with someone so childlike.
Another answer to this question is available here:
When Nick and Tom had their final encounter, Nick finally realized how childish Tom's ways where, and in return almost acted childish himself (by not shaking hands with him).
Are you asking about the plot structure for this scene or the entire novel? here it is for this scene:
Rising action: Nick "objecting" to shake hands with Tom, and accusing him of killing Gatsby
climax: Tom admitting that he had told George Wilson to kill Gatsby
Falling action: Tom talking about his grief over Myrtle, and Nick finally agreeing to shake hands