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)
"Everything Is Awesome!"
The initial situation is a society at peace. An evil, soulless, mathematically constipated society at peace. D-503 is happy with his lot as a factory approved meat computer, and he's even thrilled that the Integral is going to fly to other planets and make them all robotic too! It's kind of a unique way to start it. The bad guys aren't winning; they've won. And they won so long ago that our hero is really really blind to the crushing heartlessness it now represents. He actually thinks they're the good guys.
In short, it's a stagnant society, something calcified and toxic, and ready for things to be shaken up.
Rising Action (Conflict, Complication)
There's Something About a Girl…
I-330 starts that process of change for him. She flagrantly breaks the rules, teases and taunts him for his stuffiness, and makes him hate her so much, it must be love. The rising action is one of personal confusion, as D-503 is shaken out of his complacency and discovers his human side. This section becomes very surreal after a while, and there are chapters that might actually be dreams if you read them right. It's all about his trip away from emotionless precision and towards the messy, scary feeling place that constitute real human life. It's a long trip, and it's eventually matched by the society around him.
Climax (Crisis, Turning Point)
Revolt!
It comes to a head with the election of the Well-Doer and MEPHIS's revolt. Suddenly, all of the implied things beneath the surface come to a head. Revolution! Anarchy! Brushing without flossing! To quote Charlton Heston, "It's a madhouse!" And like the build-up, it has parallels with D-503's changes. As riots start and the Wall gets breached, D- seems to go completely ga-ga: lusting after I-330, taking pity on O-90 and experiencing various other freak-outs. In other words, D-503 is basically a human reflection of the State: what happens to it happens to him.
Falling Action
Loboto-what?
Once the revolt starts, it's a long, slow shamble towards D-503's not-particularly happy ending. In some ways, life is continuing as it always has. In others, everything has become chaos. D-503 spends this time debating with himself about what he wants. The stark choice of the Operation forces him to play his hand, but even with things falling to pieces, he embraces emotion. More importantly, he embraces the morality that emotion can bring: helping O-90 escape the city, attempting to punish U- for wrongdoing, and so on.
Resolution (Denouement)
"Everything Is Awesome?"
Sadly, it doesn't end well for D-503. He gets caught and brainwashed, and ends the book marveling at how awesome the State is. Unfortunately (from his point of view anyway) the rebellion continues, and seems to be picking up steam. So we lose our hero (sad), but gain the hope things will change for the better (good). "Hope" is about the best this can offer, unfortunately. But like I-330 says, there is no final ending. We leave the ultimate resolution of the story in doubt because to do otherwise would dishonor the ideals that the protagonists are fighting and dying for.