In this case, the publisher is J.B. Lippincott. There's no record of the publicist. The novel is To Kill a Mockingbird. The author: Harper Lee. And 50 years ago the answer was: not much.
Granted, the technology for Lee to "go viral" didn't exist, but it happened anyway. It was called "the grapevine," as in, "heard it through the."
As the rest of the Mary Murphy article goes to show, word of mouth is more powerful than any book tour or appearance on Oprah. At least, that was the case 50 years ago. But what about now? Occasionally, yes, a book will climb the bestseller list by simply word of mouth, and it's only then that the publisher starts to give it a big publicity push. Some books get a huge publicity push from the start and nothing ever really happens. Still, it's nice to think about a time when the Internet didn't exist, when people didn't friend you on Facebook just so they could then invite you to join their fan page. A time when a book was the only thing that mattered.