Decide what type of book club you want to join. There are many different kinds of book clubs. Some are comprised of members of a certain neighborhood or group (such as a church) and others have broader membership but are dedicated to a certain type of book (i.e. nonfiction, graphic novels, etc.). Decide what you want to get out of the book club. Are you looking primarily to meet new people or to explore a certain type of book.
Find a club that meets your needs. Local, independent bookstores are your best resource. Many bookstores sponsor book clubs or at least allow clubs to advertise. Find a club that interests you and contact the organizer for information on how to join.
Buy and read the club's current book. If it is a bookstore-sponsored group, the store will often have a special display for club books and may even offer them at a discount. Make sure you get the book in time to finish it. Most clubs meet once a month, so try to get the book at least a few weeks in advance.
Talk to the group's organizer and get to know the vibe of the group. Some groups take the books they read very seriously, others use them as an excuse to get together and socialize. Talking with the organizer and, if possible, other members before the first meeting will help you know what to expect.
At the first meeting, don't be shy, but don't be a bore either. People don't join book clubs to listen to long droning lectures, so don't overprepare with too many comments on the book. Just add your two cents in an unpretentious fashion and make amiable, non-book related small talk and you should fit in to the group in no time.