All necessary actions can be performed through your account's cPanel.
It's assumed you already have the new domain name registered and its Name Servers pointing to your hosting account (see orther FAQs on how to do this).
*Your primary/master account will be able to access your Sub-Domain's folder and manage it's content, but by having a separate FTP account/user for this Sub-Domain you can have someone manage the site and only have access to the Sub-Domain's content. This prevents this user from accessing your primary site's folders.