You can add permission groups to your Teamspeak 3 server on the Teamspeak client:

1. Click 'Permissions' at the top when you are logged into your server.
2. Click 'Server Groups'.
3. On the menu that comes up, click the green cross icon (it looks like a "+").
4. Type in the name of the new group.
5. Select 'Regular Group' from the dropdown menu.
6. Click 'OK'!