WordPress.org

First and foremost, you must have the Shibboleth Service Provider properly installed and working. If you don't have Shibboleth working yet, I assure you that you won't get this plugin to work. This plugin expects Shibboleth to be configured to use "lazy sessions", so ensure that you have Shibboleth configured with requireSession set to "false". Upon activation, the plugin will attempt to set the appropriate directives in WordPress's .htaccess file. If it is unable to do so, you can add this manually:

AuthType Shibboleth
Require Shibboleth

For single-user WordPress

Upload the shibboleth folder to your WordPress plugins folder (probably /wp-content/plugins), and activate it through the WordPress admin panel. Configure it from the Shibboleth settings page.

For WordPress MU

Shibboleth works equally well with WordPress MU using either vhosts or folders for blogs. Upload the shibboleth folder to your mu-plugins folder (probably /wp-content/mu-plugins). Move the file shibboleth-mu.php from the shibboleth folder up one directory so that it is in mu-plugins alongside the shibboleth folder. No need to activate it, just configure it from the Shibboleth settings page, found under "Site Admin".