Setting up unsubscribe page
You can set up a profile that includes the field Contacts > Groups.

Then send the link to that profile in edit mode, in Joomla the url will look like: http://joomla.demo.civicrm.org/index.php?option=com_civicrm&amp;task=civicrm/profile/edit&amp;gid=1&amp;reset=1

This url is the modified Create Mode (changing create to edit). To see how to get that click here

The user will need to be logged in to make changes. You can send a token in an email by adding &amp;id={contact.contact_id}&amp;{contact.checksum} to the url.