As Shmoop has said a time or two (see "Writing Style"), Dead Man Walking is not a literary, artsy-fartsy book. Mostly it says what it means and means what it says. That meaning is that the death penalty is bad. There's not a whole lot of complicated symbols or allegory going on here.
Rather than symbols, the sense-making stuff that ties the book together is often conversations with other books. The most important of these other books is the Bible. Prejean is a nun (you knew this), and she uses Biblical passages to comment on the narrative, or to think about the death penalty, or to comfort herself, or sometimes all three at once.
For instance, as Pat walks to his death, Prejean reads from Isaiah—"Do not be afraid…I have called you by your name, you are mine." (4.218) In chapter 9, she provides a lengthy discussion of the Biblical case for and against capital punishment (she decides that the case is stronger against, in case you were wondering). And so on. The words of the Bible are threaded through the book, a textual reminder of, and reference to, Prejean's faith. God's presence in Prejean's life is symbolized by the Bible's words in her book.