Usually the Web service providers setting up CPanel for your administration purpose also provide FTP access primarily used for uploading, modification and support of your Web sites. Alternatively, you usually can have an access to some Web-based "File Manager", but this option is just not serious.
If your provider does not provide you with FTP access to your sites, you are in a
big trouble. Ask them to provide it, and in case this is a problem,
abandon this provider as soon as possible and transfer the site to a decent provider. You always can find something better and sometimes even less expensive.
Now, just in case: if you self-host your sites on your own Linux host (I don't think you do though), install and configure some decent FTP server, create accounts, etc., and use it for site support.
There are some other — secure — options:
http://en.wikipedia.org/wiki/Secure_FTP#Secure_FTP[
^].
—SA
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