Upload the folder simple-google-sitemap to the /wp-content/plugins/ directory
Create an empty file sitemap.xml in your blogs root folder and make it writeable (chmod 666).
Activate the plugin through the 'Plugins' menu in WordPress
Edit and save the Simple Sitemap options in the admin panel and create your first sitemap. You can browse the result at http://your.blog.tld/sitemap.xml.
Nothing else to do. From now on, the plugin creates a new sitemap whenever you publish or delete an article and Google will be notified about the new sitemap.