I discovered a great extension which can clone or backup your Joomla 3.x site.
It is called Akeeba Backup and the extension is found here.
Just upload it to your existing Joomla 3.x site and you can then access it through Components on your admin site.
If you make a copy of your, for example, development site you can easily transfer the jpa-backupfile to your new site. Just upload this file to the root of your webserver installationfolder, for example /var/www on a apache webserver. You also have to transer a few files which are included in Akeeba Kickstart found here. Just place the required files from the kickstart-zipfile at the same folderlevel as the jpa-file.