What's your domain?
If it's a WordPress site, you can refer to this article for help: http://codex.wordpress.org/Changing_The_Site_URL
For a non-WordPress site, if all your links are hardcoded to use mysite.com/new/whateverpage.php for example, you will need to go and edit all the links in your code to take out the /new part. Once that part is ready and all the parts of your site knows to use mysite.com/page.php rather than mysite.com/new/page.php (for example), you could go one of two ways:
Use an FTP client to drag /new outside of /mysite.com, and then change the names.
OR, click "Edit" for the domain in our panel, and in the Fully Hosted settings, change the site directory to be mysite.com/new
That second option would simply tell the domain to look straight at that /new sub-dir for the main site content. Anything in any directory above it will be ignored, except for any .htaccess files because those work recursively.