The way the family library feature is supposed to work is that one person sets themselves up as a manager of a family account, and then invites other members. The members share content and the payment method, while the manager runs the group (which is limited to six people).
Or as Slashgear said:
A family can be a group of up to 6 individuals that have to be living in the same country. At least one of those should be above 18 years of age and have a valid credit card, because that one becomes the family manager. That manager has the responsibility of setting up the payment method and controlling which content can be shared. The rest of the members need to have Google Play Accounts, of course, but those can’t be work or school accounts. Plus, they can only be a member of one family at a time. Amusingly enough, they can switch to another family only once per year.
Once set up, any family member can use the family payment method to buy apps, books, movies, and whatnot. That does mean that, except for underage members and in-app purchases, family managers can’t really block a purchase, as they will only be informed after the purchase has been made. They can, of course, request a refund.
In reality there’s no family library feature for Play Books – at this time. There’s no family library feature for apps. Really, there’s no family library feature for anything other than Play Music – and only on Android.
The thing is, you have to subscribe to Play Music on Android (not iOS or the web browser) before you can utilize the family library feature. Once you’ve subscribed you can share purchases, but if you don’t want to subscribe or if you don’t use Android then the feature doesn’t exist.
As someone who sometimes reads ebooks in Play Books, there’s no way for me to test this feature without paying ten bucks a month, and that has to be the dumbest way to set up a “family library” possible.