Each family member has to have a separate username and password. So the first step is to create the new accounts (if you haven't already).
I suggest creating it with an email address (not the one used for fb, if possible), since you'll be able to pick a spotify username / password. Using facebook will not let you do that, and that sometimes causes problems.
Send the invites to the email you used to create your new accounts. Accept the invites and you'll be set. Everyone will be able to listen to music at the same time, and will have separate libraries, playlists and friends.