Most good stories start with a fundamental list of ingredients: the initial situation, conflict, complication, climax, suspense, denouement, and conclusion. Great writers sometimes shake up the recipe and add some spice.
Initial Situation
Bartleby arrives at the Narrator's law practice, seeking employment.
Initially, everything seems normal; Bartleby, the new guy, shows up at an already-established office, and immediately gets to work. Nothing too weird exhibits itself, and though Bartleby is oddly quiet, the Narrator finds this a relief, compared to the eccentricities of Nippers and Turkey. We're not sure what can possibly occasion the Narrator's story, since business seems to go on as usual after Bartleby's arrival on the scene…for a little while, at least.
Conflict
Bartleby "prefers not to" examine a paper with the Narrator.
Huh. This is our first taste of the truly bizarre nature of this story – Bartleby, who has been a solid employee up to this point, refuses point-blank to obey a simple order. Everyone is mystified (except Bartleby, that is). He continues to "prefer not to" do anything but copy documents, even when the smallest favors are asked of him. We're not sure what to make of this refusal, and neither is the Narrator.
Complication
Bartleby "gives up" work and is fired…sort of.
Eventually, Bartleby just stops working at all. This gives the Narrator reason to fire him, which he attempts to do. However, Bartleby prefers not to leave the building, and continues to live there, which understandably creeps out clients and visitors. Again, Bartleby's motives are totally obscure. Why does he prefer to stay in such an uncomfortable environment? We honestly have no idea.
Climax
Unable to get rid of Bartleby, the Narrator moves to another building.
Bartleby ultimately wins in the odd, rather one-sided struggle between him and the Narrator. When the scrivener just won't leave, the Narrator picks up and moves his whole practice to another building, just to get away from Bartleby. This is, admittedly, a pretty wussy and really impractical way to "resolve" the problem.
Suspense
Bartleby continues to haunt the Narrator's old office.
The suspense and confusion builds as we learn that Bartleby remains at the office, even when its occupants leave. Apparently, he continues his wall-staring, resistant behavior even when a new law practice moves in; we have to wonder, rather anxiously, how long he can keep this up, against the opposition of an increasingly large crowd of enemies.
Denouement
Bartleby is taken to prison.
The conventional problem in the text is resolved when Bartleby is simply removed from the building; he doesn't even put up a fight when the police take him to prison. While this looks kind of like the end of the story, it's really not. This "denouement" is a false one, and while things seem to have been cleared up, the central problem of Bartleby has simply been pushed aside, but not resolved.
Conclusion
Bartleby dies.
In a final act of protest, Bartleby refuses to eat, and subsequently starves to death in prison. By just preferring not to live any longer, Bartleby announces his individuality in an ultimately fatal, dramatic fashion: if he cannot live as he "prefers" to, he apparently doesn't want to live at all. In the end, we don't know what it was that Bartleby "preferred," and we are left to ponder the mystery of his death.