Unzip the module, and move the module root tree striped of the version number into the /var/www/drupal/sites/all/modules
In the case of a Dependency Library unzip it and move it into the library location: /var/www/drupal/sites/all/libraries
fix the permissions on the module to: chown -R www-data:www-data
Enable the uploaded module by navigating to base-site-url/admin/modules, scrolling down to the Module (in the 'Islandora' category), checking the box to the left of it, and then scrolling to the bottom of the page and clicking the 'Save configuration' button.
Once installed, configuration options for the Islandora module in question can be found on your site at http://path.to.your.site/admin/islandora/configure
Once configurated, you should be able to test the module. Ensure that the 'testing' module is enabled in Drupal (it is not by default), then go to Configuration -> Development -> Testing and click the link.
This will pop up a new window with a list of tests to run. Scroll down to the module in question, then click the checkbox. Scroll down to the bottom and click "Run Tests".
You may want to start will all the remaining Solution Packs first, and add the dependency modules as required.