You can add permission groups to your Teamspeak 3 server on the Teamspeak client:
- Click 'Permissions' at the top when you are logged into your server.
- Click 'Server Groups'.
- On the menu that comes up, click the green cross icon (it looks like a "+").
- Type in the name of the new group.
- Select 'Regular Group' from the dropdown menu.
- Click 'OK'!