It would be great to have a different password for the users of a Family Premium Account than the password that is used to manage the account, especially billing information. This would prevent kids making nefarious changes.
Each family member has to have a separate username and password, so the first step is to create new accounts for each new member (if they haven't already).
I suggest creating it with an email address (not the one used for Facebook, if possible), since they'll be able to get a Spotify username / password. Using Facebook will not let you do that.
Each member will now have a Free account, so the next step is for them to join your Family plan through your account (You're the one who pays, so you'll be the Family Admin).
Let them accept the invite logged in with their own username in the app and in the website. They should make sure to type the address exactly as the Admin did when he created the Family Plan, and also be sure all Family members use the same Internet connection (Home network) regularly.
Each will be able to listen to music at the same time, and will have separate libraries, playlists and friends.