There's two parts of the site you must backup. The file system, and the database.
To backup the file system use an FTP client such as
FileZilla. I don't recommend using web based file managers for anything other than rudimentary file manipulation.
You should be able to backup your database from your hosting control panel. This would normally be done with an application called phpMyAdmin. Have a look on the net for the manual for phpMyAdmin and check out it's export functions. You could also install a Zen mod to enable you to do this from your store's admin panel.