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
The brothers return to Skotoprigonyevsk.
The brothers find themselves back in or near their father's home, for vastly different reasons. All that Karamazovian fury concentrated in one locale leads to an incredibly volatile situation where desire, greed, pride, and resentment explode into murder.
Conflict
Dmitri and Fyodor have a dispute over Dmitri's inheritance and are romantic rivals for the same woman. Meanwhile, Ivan is tormented by Smerdyakov's sly suggestions, and Alyosha worries over the elder Zosima's declining health.
The real engine for the conflict is Fyodor Karamazov, the father. This wily, dirty old man cons Dmitri out of his inheritance and attempts to seduce his love interest. But Dmitri isn't the only one out for a piece of the Karamazov fortune: Smerdyakov is around to slyly remind Ivan that he, too, has a vested interest in Fyodor's death. Meanwhile, the monkish Alyosha doesn't understand why his elder insists that he attend to his brothers instead of his monastic duties, especially when his elder is so near death.
Complication
After Ivan leaves town, the elder Zosima dies, leaving Alyosha distraught. Meanwhile, Dmitri scours the town in search of someone to lend him 3,000 roubles. He fails.
Ivan seems to have escaped Smerdyakov's sly plans by leaving town, and Alyosha finds his faith temporarily shaken by Zosima's death. Dmitri desperately seeks a loan of 3,000 roubles, believing the sum will enable him to claim Grushenka for himself, and also to settle a debt of honor with his former fiancée.
Climax
Fyodor Karamazov is murdered.
The death of Fyodor, the man causing so much trouble for his sons, determines the rest of the action of the novel. It's also interesting that we never see Fyodor murdered; there's a break where the murder should be. Oddly this makes the murder even more climactic, because we genuinely don't know, can't know, what happened to Fyodor until hundreds of pages later...and that's called suspense. Which takes us to the next stage . . .
Suspense
Dmitri is falsely accused of his father's murder and is put on trial. Alyosha and Ivan work in very different ways to assist Dmitri in his defense.
Because Smerdyakov confesses to the murder on the evening before the trial, the suspense of the trial scenes consists in whether Dmitri will be convicted or saved by the truth.
Denouement
Dmitri is convicted of his father's murder and awaits his deportation to Siberia. His brothers and former fiancée work on an escape plan.
The truth loses out: nobody believes Ivan when he relates Smerdyakov's confession, and Dmitri is found guilty. While his brothers work for his escape, Dmitri welcomes the possibility of becoming a "new man," purified by the experience of suffering.
Conclusion
Alyosha joins the boys of the town and the Snegiryovs to mourn Ilyusha's death.
The conclusion of the novel finds Alyosha at Ilyusha's funeral. Surrounded by Ilyusha's friends and united by their love, Alyosha asks them all to remember this moment of shared goodness.