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.
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.
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.
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 . . .
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.
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.
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.