$this->applications = array();
//line to add under
        $this->add_application(new new_module_app());

this should do the trick, the position of your tab depends on which line you added your module.
you also need to redefine add_module(), add_lapp_function() and >add_rapp_function() in ordre to show blocks and links in your module.
define also the access levels for your pages in access_levels.inc (includes folder).