Due to the nature of the Advanced Tools system, installation requires write access to the normal parts of your site, however to install the Library and Package installers requires specific write access to the following directory:

/libraries/joomla/installer/adapters

Please note that if you want to use the update manager, you will need to have your entire Joomla! site writeable otherwise updates will fail.

The entire Advanced tools package is installed via a regular component. Once you have set up your permissions properly, use the normal installer to complete installation.