There are three (possibly four) parts to this.
- Back up your server
- Change the DocumentRoot of your web server configuration, so that it serves the "moodle" directory as root, instead of the parent directory of "moodle";
- Change the $wwwroot value in moodle's config.php from "www.websitename.com/moodle" to "www.websitename.com";
- Depending on how much work you have done in Moodle (basically whether you have defined internal URLs as activities, made links to internal pages within the site in any of your descriptive text on the site, or installed plugins that store links in the database using hardcoded references, for instance) you may have to go to www.websitename.com/admin/tool/replace and run the script there to replace your old URL with your new one. Note that this is an unsupported script, it generally works fine, but you should always do a back up before running it just in case.