If you want to edit an object (node id 512) directly on you public siteaccess, go to the url /content/edit/512.
You'll see the standard edit.tpl there.
The second step is to override the standard design/standard/templates/content/edit.tpl for your public siteaccess within the settings/siteaccess/your_site/override.ini.append.php and to create your own edit.tpl
You can create different edit templates for different sections, classes, nodes, ...
Take a look at the documentation under
http://ez.no/doc/ez_publish/technical_manual/3_8/reference/template_functions/visualization there you can find the attribute view gui which you can use to create custom edit templates within your public interface.