WordPress.org

1. Unzip into your /wp-content/plugins/ directory. If you're uploading it make sure to upload the top-level folder. Don't just upload all the php files and put them in /wp-content/plugins/.
2. Activate the plugin through the 'Plugins' menu in WordPress
3. Visit your options (Options - Broken Links Remover) for Wordpress 2.3.x, (Settings - Broken Links Remover) for Wordpress 2.5.x

If you have to upgrade manually simply repeat the installation steps.