See this guide on how to backup your site:
How to manually backup your site.
You can use this to get your files and databases so you may transfer them to the other host. After you are done, you may either keep your hosting account here (I'd recommend this just in case the other host doesn't work out for you), or delete your free hosting account by copy/pasting the following in a reply and filling out the required information (cPanel username and inserting an X in the parenthesis). Note that we can only delete free hosting accounts, we cannot and will not delete forum accounts:
cPanel username:
( ) Inserting an X inside the parentheses signifies that I have made all necessary backups of my free hosting account and will not hold x10Hosting responsible for any data I am unable to recover after my free hosting account is deleted. The X also serves as my digital signature verifying that I have proper authorization to request account deletion of the account specified.