To get more members for your family, other members have to apply for membership. They just have to visit the family profile page and click on the button “apply for membership” to send you their request.
A little red digit will tell you, if another player has applied for membership with your family. Open your family page and click on the pen next to the player name to accept or decline membership. Via this pen you will also be able to change the status of a family-member after he or she has joined the family.
To get new members, simply write them a personal message and advertise for your family, so that they apply for membership.