Dead Man Walking is actually mostly about a live woman walking: Sister Helen Prejean, who's the writer and the narrator and the spiritual center of the book. She may not actually look much like Susan Sarandon, but the story is about her, anyway.
So, Prejean is totally a nun working in the New Orleans housing projects and teaching high school dropouts, because this is the kind of socially active thing nuns in her sisterhood have decided to do. A member of the Prison Coalition asks her to be pen pals with Patrick Sonnier, an inmate on Death Row who has been convicted, along with his brother, of a horrific rape and double murder. She agrees. Consequences follow.
Prejean meets with Pat and learns the details of his case. She also meets his brother, Eddie, who it seems likely is the one who actually pulled the trigger to kill the two teens, David LeBlanc and Loretta Bourque. Prejean becomes more and more involved in the details of the case and begins working with lawyer Millard Farmer to try to get Pat's sentence commuted to life in prison.
Spoiler: she fails. Pat's executed—though as his spiritual advisor, she manages to get him to reconcile himself to his death and to offer words of apology and forgiveness at the very end of his life. With his last words, he says he loves her. Prejean watches as Pat is put to death.
As you'd imagine, this is extremely upsetting, and though Prejean is committed to trying to change the death penalty, she never wants to be a spiritual advisor again. But not long after this, she's asked by Millard Farmer to advise Robert Lee Willie, a Death Row inmate convicted of the rape and murder of an 18-year-old girl named Faith Hathaway. Prejean says yes, she'll be this dude's spiritual advisor because, well, that's the sort of thing you do if you're a social advocate nun.
With Pat, Prejean did not contact the families of his victims. They were hurt and wondered what the Catholic Church was doing supporting murderers. Prejean feels she did the right thing in working against the death penalty, but she also feels that she needs to work to try to help victims, too, so she reaches out to the parents of Robert Lee Willie's victim Faith.
Prejean's relationship with Faith's family is difficult, but she eventually becomes good friends with Vernon Harvey and Elizabeth, even though they are enthusiastic supporters of the death penalty. (Vernon says at one point that he and Prejean are like friends who root for opposing baseball teams, which doesn't seem quite, quite, right, but it's close enough.)
Anyway, Robert Lee Willie is much less likable than Pat Sonnier. In media interviews, for example, he boasts about being a fan of Hitler. On top of that, he's a lot less remorseful about his horrible crime than Pat was. Nevertheless, Prejean works to get him to accept responsibility, and she tries to convince him that his life has dignity and worth. She also works to try to get his sentence commuted to life in prison.
Spoiler: she fails. He is executed.
The book has kind of a grim inevitability to it.
After the execution, Prejean becomes closer to the Harveys. She continues to work for the abolition of the death penalty, and, thanks to the Harveys, she also tries to work to get better treatment for victims by law enforcement.
So… as you may have noticed in this quick synopsis, the plot doesn't really work like you'd expect it to from a novel, or even from a lot of nonfiction books. The point of the book, though, isn't really the plot; the events in the book are mostly meant to be examples, or persuasions. They're part of a case against the death penalty, which includes statistics, quotations, and other examples.
At the same time, though, even though they doesn't exactly carry the book, the stories of Pat and Willie and their victims' families are vital to what Prejean is trying to do. The book has to be a memoir, not just an argument, because Prejean wants you to see that people are involved on both sides. She wants you to sympathize with the victims and their families, but she also wants you to witness the executions, and she wants you to understand that when the state kills, it kills a human being, with relatives and family, and with dignity, no matter what awful things he might have done.