From what I've heard, being in a book club can be frustrating. I have to admit that I've never joined one; as someone who reads, teaches, and writes about literature for a living, I've restricted myself to professional "reading groups" with the assumption that, when I have free time, I might do myself and my family a favor by cultivating interests outside the literary and critical realms. (Whether I've succeeded is another question.)
But based on reports from several people who've attended multiple book club meetings, hoping for intense or at least engaged literary discussions, it seems I'm not always missing much. The experience of diligently reading a text that you didn't necessarily choose, only to find that everyone else in one's book club is much more interested in talking about their kids, work, or at best whether they "liked" the book in vague terms, seems common -- and demoralizing. If you can't get people in a book club to talk about literature in a sustained and involved way, where can you hope for a good literary discussion outside a classroom?
Book-club culture has a long and distinguished history going back at least to the coffeehouses of 18th century London and the literary salons of 19th century Paris. The following "talking points" are intended to help focus and enliven the conversation in any book club serious about discussing literature (which for purposes of clarity I'm going to assume means novels, although obviously other books are fair game too).
1. Try to talk about the book, not around the book. Ideally, book clubs are different from other kinds of clubs because they bring people together around, well, books. If you don't really want to talk about books, maybe you should consider joining another kind of group.
2. Plot, character, setting, and style are the four basic formal elements of any novel. (I've discussed some of these before, here and here.) As long as you are describing, considering, analyzing, or asking questions about one or more of these elements, you can be sure you are staying focused on the book that everyone (presumably) has read and gathered to discuss.
3. When considering context, try to keep it relevant. All novels are written, to a greater or lesser extent, in dialogue with the author's historical era and social milieu. You don't need to be an expert on 1920s America to read The Great Gatsby, for example, but it doesn't hurt to know a little about the Jazz Age in order to make some more informed speculations about what F. Scott Fitzgerald is trying to accomplish in the novel.
4. When passing judgment, whether aesthetic or moral, on a book, try to remember the circumstances in which it was written. This includes not just the author's biography, and not just the historical period and cultural situation in which the book was written, but also the likely intended audience for the book. If you're reading 19th century fiction, for example a "sensation novel" like Wilkie Collins' The Woman in White, complaints about its relatively slow pacing compared to today's page-turners should be mitigated be trying to figure out what elements of the book might have made it attractive, even downright provocative, for its original readers.
5. The author's biography and recorded statements about what s/he wrote are important, but they are not the whole story. We are well past the period in literary criticism, known as The New Criticism, in which texts were considered to be gloriously isolated artistic creations, and all talk of the author was forbidden. Nevertheless, too much speculation on the author's intentions tends to stifle dialogue, and is often simply a cover for ad hominem attacks. The same goes for limiting the conversation to the author's own interpretations of his/her writing. After all, if words never expressed anything more than their speaker's direct intentions, not only would psychoanalysis never provide insight into unconscious motivations and desires, but also irony, ambiguity, and Reader-Response Criticism would be non-existent.
6. Don't ignore intertextuality -- allusions to or echoes of other books -- but don't limit yourself to it either. Saying that Ian McEwan's Atonement reminds you of Jane Austen's Mansfield Park is perfectly legitimate, especially when you can point to specific passages or plot points that set up such echoes. But repeatedly saying "Book X reminds me of Book Y" is not only of limited interest to others, it's potentially insulting to everyone's intelligences. The overuse of personal anecdotes ("Chapter Three reminds me of that time when I ...") falls into the same category, I'm afraid.
7. For an interpretation to be valid, it has to be convincing to someone other than you and your immediate family! You may have an opinion about a character's motivations (altruistic or self-serving? pragmatic or cowardly?) or a plot twist (believable or sensational?), but unless you can articulate your reasons -- usually by finding evidence in the text to support it -- what you've really got is a feeling or reaction, not an interpretation.
I've just set out a few "rules of the road" that I think any book club would do well to keep in mind when proceeding. There is no greater social pleasure than discussing a book with others who have read it as well. The books we read are frequently the narratives we live by and learn with. Our discussions of them should be at least as rewarding as the stories themselves.