Within book clubs and communities you'll find the ability to participate in discussions. There will be a discussion thread box on the page like this:

It shows the various discussion threads created, and you can click through to each to read them and post your own comments.

In the discussion threads box you'll see the usual Connections 'add' icon, which you should click to create a new thread. Enter the title of the discussion thread when prompted by the pop-up:

When you've entered the title and created the thread, you'll be taken to the thread itself to post the first message.

Once you have opened a discussion thread, you can read all the posts within it, or add a new message by entering it in the text box at the bottom:

As part of a book club or community, you automatically follow discussion threads when joining that club/community. Therefore when new threads are created, or users post in threads, you'll see alerts in your 'My Following' box: