How do I add a new template to my site

You can install a File Manager within WordPress, Search the Plugins.

Or the easyist way to be honest is simply login via FTP to your web host locate the template folder within wp-content/themes/yourtheme/ and create a file with the name you want to have it. i.e wp-content/themes/yourtheme/mycustom.php just insert in the empty file. and then your see it editable within the theme editor.

Hope this helps you out.