While I did not lead a book club, I was second in-command in two and I, currently, lead a study group as an undergraduate. Here's what I learned in both experiences.
You should always keep in mind how many members you want. Maintaining a book club with 4 to 7 members is easy because you can get to know each member individually, and you can keep tabs on who's coming to the meetings and who isn't. Larger groups take more work, and inevitably attendance will drop because each member will be contributing less and less as the group grows, so they don't really get attached to the group.
Some people have great intuition, some don't. Follow yours if it has yielded good results before. If it hasn't, find someone on whose intuition you can trust.
Example: In one of the book clubs I assisted, the leader was easily influenced by flattering. I met one of the possible recruits and I was immediately struck by how unsettling he was. He did not seem trustworthy at all. Later I discovered he had many rape accusations on him, among other illegal activities. He took over the discussion and derailed the entire group, and after I left all the female members left because of how unsafe they felt around him.
Quality is harder to achieve than quantity. Once you have achieved a number of members slightly higher than the ideal, cease recruitment and focus on improving quality of the research/debate.
Some people will drop out and that's OK. It's inevitable.
On the Group's Structure
Ideally, you should at least have a second in-command. Someone who can share some your responsibilities, who understands the group's missions and objectives, who can recruit and evaluate members, who can take decisions in your absence.
Each member will eventually show his or hers personal skills and tendencies, and you'll have to watch out for that. You might have a member particularly prone to joking and changing the subject, and that can be good if he or she raises morale when everyone is tired of debating. You might have someone who likes cooking for the group, which brings many benefits. Someone might have a great place where you can bring everyone to discuss the book. And, of course, everyone has negative points and you have to deal with that as well. And so on.
Example: I recruited a young man to my research team. I already knew him for some time, and knew that he struggled with a deep depression, that he had a terrible family environment and that, while hard working, he struggled with his grades.
At first, he lagged behind and was a constant drain on my time and resources, which made me reconsider my decision of accepting him on the group. As of now, though, he is our most dedicated researcher and one of the few people I always seek when in doubt about how to manage the group. He is, now, my assistant and most loyal researcher.
You don't need to know everything about the subject, but it's unforgivable if you come across as knowing more than you really do. Set your boundaries, clarify how inexperienced you are. You are an undergraduate and no one should forget that.
Still, you absolutely need to know how to lead a discussion so that people expose their thoughts and experiences. You'll need some charisma for that, and it often helps if you know each member individually, even if superficially.
Example: I am an undergraduate and I lead a research team. One of our members, hierarchically inferior to me, is someone with years of experience in the area. She alone has more publications than everyone else in the group together.
Still, she has never questioned my authority. Because I lead the group well enough, because we work great together, and, mostly, because I know when to shut up. She knows more than I do, so I let her talk without interruptions.
Get to know you book club members. Some will be shier, some more vocal, and that has nothing to do with the quality of their contributions. Learn how to make the shy genius speak, and control the vocal minority who often derails the discussion. Control the debate so that everyone contributes, otherwise you'll be bleeding members after some sessions.
Eventually, every group develops a culture. Respect and cherish it.
Example: On my research team we often organize lectures. Our marketing is often humorous, it's our opportunity to joke about our research. Most of our attendants comment that our relaxed approach to the subject matter was a deciding factor in attending our events.
On the Meeting
Prepare a list of subjects to be discussed and send it to the members some days before the meeting. After the meeting, send a summary of what was discussed and decided.
If the meeting is going for too long, make a short break to drink water, eat something and use the facilities.
Try to make the meeting someplace where you won't be interrupted or bothered. Be there some time before the expected time so you can make sure everything is there (number of chairs and tables, for instance.)
If someone is not taking part in the debate, ask for their opinion on the subject. Try to make everyone participate.