Comment 1 for bug 269109

This issue has been solved in the upcoming release.

If you are using the current release and would like to fix it, follow these steps:
- login as root, password turnkey
- chown www-data: /var/lib/joomla15/tmp
- chown www-data: /usr/share/joomla15/modules
- chown www-data: /usr/share/joomla15/templates
- chown www-data: /usr/share/joomla15/plugins
- chown www-data: /usr/share/joomla15/language

Unfortunately this is the best fix I could find according to the Joomla documentation.
If anyone is aware of a better, or a way to install user extentions in a different location than core, please post a comment here.