If you go to your CPanel there should be an icon or link that says something like 'Password Protection'.
The interface for the password protection is kinda weird and takes a little getting used to. Basically, you click the *icon* of the folder to navigate and the *name* of the folder to bring up it's protection options. First add a user (make sure you put both the name and the password - the interface for changing user passwords later is worse (at least in Mozilla, maybe it's different in IE?). Once you have entered a user you can enter a name for the 'Protected Resource' (i.e. My Subdomain Protection) and check the box 'Folder requires a password to access via http:/'
That should do it for the protection. Oh, BTW the interface problems are not *****'s fault, it's the issue of CPanel's creators.
HTH,