What is the plot of The Curious Case of Benjamin Button?

 

Beginning:
The narrator refers to an "astonishing story" he is about to tell, and we know that it has to do with Mr. Button's first born.
Rising action leading to conflict:
Benjamin Button is born and they realize his face is that of an old man. He is rejected by his father, and society as a whole rejects him. However, he is taken in a retirement home, where he is with his "equals".
Continuing action:
The story is not narrated directly stating that BB is actually getting younger, but as the story grows, even the main character is surprised by this fact, as so is the reader.
Climax:
There are several intense moments in the story, from the moment he met Hildegarde to when he was found as a young kid. For a short story, this is not as common, and it is very hard to determine. However, the meeting with H. was what probably created the most suspense prior to its happening.
Falling Action
The falling action must be after his wedding to Hildegarde, because everything after that points out to his making the choice of battling what curses him, and facing it. He knew what was going to happen next, and that at some point he would have to abandon her. We also know that, the younger he gets, the closest he is to death. '
Conclusion/End
Benjamin does get younger and younger until his life ends.
The end is difficult to discern because of the way the author narrates it. He makes death look like a transition much like birth: It involves light and darkness, basic emotions and feelings, and the fact that he simply forgot everything prior, because now he is a newborn (about to die).
It is interesting, however, how life and death mirror each other in description. It is perhaps the moment of the story to which somehow we can relate:

There were no troublesome memories in his childish sleep; no token came to him of his brave days at college, of the glittering years when he flustered the hearts of many girls. There were only the white, safe walls of his crib and Nana and a man who came to see him sometimes, and a great big orange ball that Nana pointed at just before his twilight bed hour and called "sun."

[…]

And then he remembered nothing. When he was hungry he cried—that was all. Through the noons and nights he breathed and over him there were soft mumblings and murmurings that he scarcely heard, and faintly differentiated smells, and light and darkness.