From Joomla 3.2, a "Super User" logged into the frontend should be able to edit website modules. This is a great feature that enable you to update the website without accessing the Joomla backend.
In order to use this feature you first need to enable that feature in "Global Configuration"
You can see the configuration setting in the image below, it is called "Mouse-over Edit Icons for........." as you see of the image below I have chosen to activat this feature for both modules and menus. (click on image to expand).
After that setting is configured, a user loggedon to the frontend should be able to see the edit button when hovering over a module on the site.
HOWEVER, if you like me are using Artisteer as your template creation tool, then you will still have a problem as Artisteer out of the box does not support the feature.
You will therefore have to add some additional code in Artisteer under the "Export options" - "CSS Options"
The code to be added is:
{spic}.icon-edit:before { content: url('/../images/system/edit.png'); }{/spic}
See picture below (click on image to expand):
Finally you need to save and export your amended template, and then install and activate this, and viola, you should now be able to use the new "Frontend Module Editing" feature on your Joomla website.