It’s an old threat, but maybe it will help somebody.
A very easy to use tool for this is Akeeba. http://extensions.joomla.org/extensions/access-a-security/site-security/backup/1606
Just install it, make a backup, download the backup files to your pc, or just upload them from your old site to your new site through the build in FTP option. Then you need to upload 1 extra file named kickstart. Go to the new site url with /kickstart and follow the steps.
You will see that it is very easy, the most time you need for the down/uploading of the backup files.
