See upstream README file for configuration and usage instruction.
Almost all information from that file is relevant.  However, the
content below replaces the "INSTALLATION" section:

  * Initialize the database

      rt-setup-database-5 --action insert --datafile \
         /usr/share/request-tracker5/plugins/RT-Extension-Nagios/etc/initialdata

    Only run this the first time you install this module.

    If you run this twice, you may end up with duplicate data in your
    database.

    If you are upgrading this module, check for upgrading instructions
    in case changes need to be made to your database.

  * Edit a file like e.g. /etc/request-tracker5/RT_SiteConfig.d/90-local.pm
    and add the line:

      Plugin('RT::Extension::Nagios');

  * Restart your webserver or FCGI runtime.