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.
Exposition (Initial Situation): Bye-Bye, Feudalism
The Manifesto picks up the story of the workers as European serfdom comes to its dying gasp around the 18th century or so. It's a time period (in a galaxy far, far away...) when the bourgeoisie is rising in power against the aristocracy. And pretty quick—like, you know, just a few paragraphs into the manifesto—the bourgeoisie becomes the most powerful class, and it's busy oppressing the proletariat—the workers—as the aristocracy fades away.
Rising Action (Conflict, Complication): Workers Join Together
So we have a big conflict between rich and the workforce: "two great hostile camps [...] two great classes directly facing each others: Bourgeoisie and Proletariat" (Section1.5). Pretty soon, individual laborers, and then the workers at individual workplaces, rebel at times. For example, they might fire to a factory to protest their working conditions (Section1.36).
Now, the rich keep winning (Section1.37), but then groups of workers start unionizing and growing in number and feeling their strength more and more (Section1.37-38). The real victory of the battles is that proletarians learn to cooperate with each other instead of competing with each other (Section1.39). They even form political parties (Section1.40).
Climax (Crisis, Turning Point): Team Revolution Wins!
Eventually, the proletariat seizes power, by violent revolution if necessary (Section1.51). With the workers in power, everything should go smoothly.
Falling Action: Transitional Government
The proletariat sets up a temporary government—a.k.a. a vanguard state—in order to transition the society from capitalism to communism (Section2.68-71). It's a centralized government that takes capital away from the bourgeoisie, by degrees, and puts the means of production into the hands of the community. This is supposed to bring about an end to class distinctions, allowing a new world where, as Marx put it elsewhere, the organizing principle would be: From each according to their ability, to each according to their need.
Resolution (Denouement): Here We Go Again?
In past communist practice, some vanguard states have led to governments that don't disappear but instead function dictatorially, like the Soviet Union under Josef Stalin. The historical origin of the word revolution calls to mind the image of the wheel of fortune, turning the bottom to the top and the top to the bottom, over and over again, endlessly. Will the workforce simply become the new bosses if they take over? The saying exists for a reason: Meet the new boss, same as the old boss.