I joined one that has been going a long time. Every month (usually the second Thursday but it's flexible depending on what everyone is doing) we meet at someone's house. Almost always the same person, largely as she has space. There are 12 of us. She normally lays on tea and coffee. (I ought to say that most of the members are retired - the eldest is 90. I am 41 so quite a bit younger than most of them but it means that our book club is run to meet their needs - we don't meet in the pub for example!). We don't meet in the summer when lots of people are away or busy with family. And often in January we have a poetry meeting - instead of reading a book over Christmas, we all bring a poem (we have a theme) to read out and discuss, as a lot of them are busy with family etc.
We chat for a bit, then bring out the book. Someone will have been asked to 'introduce' it. Means doing a bit of research - the author's life, what were their famous works, if any, and are there any interviews about the book we've read which might give a bit of context or ideas about where the inspiration for it comes from. Usually this lasts between 5 and 10 minutes - really depends on the author and the book! Then people jump in and we just chat - who liked it, who didn't. Why or why not. What you thought of different characters, was it believable, funny etc. Often ends up with people sharing different memories from their own lives, especially if we've read a book set in an era which means something to someone.
We've read a huge range of books - we read a book by Claire Tomalin about Samuel Pepys, which was excellent, and we've read the first of the Cazalet Chronicles, and a book called The Eyre Affair by Jasper Fforde, and classics like Jane Eyre.
We get our books through the library. They have a service where they have about 500 titles, and they have multiple copies of them (usually 12). We have one person co-ordinating things with the library - me, at the moment. So, I will look through the list, available online, and choose books I think might appeal. It's just titles and authors so sometimes it's a stab in the dark! The others have had the list before but mostly are happy to let someone else choose! Then, at some stage before the date of the meeting, I go to the library, pick up a set of books, take them to the meeting, we have the discussion about the book we've just read, and then I take in those books and hand out the books for next month.
We live in rural Cornwall so I don't know if this service is available elsewhere. We also all live fairly close to each other and so if someone hasn't finished the last book and wants to hold onto it, and drop it back to my house when they are done, that's fine by me. I keep lists of who has had a book given to them and who has returned one! Organising it can be interesting. I have no idea how many other book groups are waiting for a particular book, so I usually have three or four on order to make sure we have at least one ready to collect and read. The library are really laid back about when books get returned, thank goodness.
Works for us. Hope that all helps!