Some following is automatic, e.g. when you become friends with someone, you automatically follow all their events (adding books, reviews, etc). Also when you join a book club, you automatically follow the club's events (adding items, scheduling meetings, etc).
You can choose to follow additional aspects of Connections, e.g. a user (by going to their profile and clicking the “follow this user” icon) or an item (again you'll see the same icon):
On a user profile, the “My following” box will show the latest five events that the user has chosen to follow:
Once you click on “Show more”, you will see a lot more information about your following:
In the “My following” settings you can choose: