First you will need ensure that your CPanel hosting account includes additional domains.
To add an addon domain:
1.Enter the domain for the new addon domain into the New Domain Name field.
2.Enter the main FTP username for the addon domain in the Subdomain/Ftp Username field.
3.In the Document Root field, enter the directory that will contain the addon domain’s files.
4.Enter the password for the addon domain into the Password fiel making sure you use a secure password.
5.Confirm the password in the Password (Again) field.
6.Click Add Domain
7.To add files to the addon domain’s home directory, click the File Manager link.
Now to FTP to the new addon domain to upload your site:
For example, if you made an addon domain called: mynewdomain.com and in the second box you made a new Username/directory/subdomain Name called: mynew
with the password: somepass, then you would have a separate FTP account that only allows access to the "mynew" folder. This is nice if you want to restrict access to your primary site.
You would then login to the FTP site as:
ftp host: ftp.mynewdomain.com
user: mynew@maindomain.com
pass: passwordyouset
You can also simply FTP to the main site, using the main site's username and password, then upload the files as you would to any regular subdirectory, but the "mynew" subdirectory acts as public_html for the new site. I find that way easier but I find a separate hosting account the easiest.
For cPanel, you cannot access a separate cPanel for the new site, that is only possible with a reseller account.
The way to access the new site's cPanel is via the main site's cPanel, then if you have a look around, you see options now for both domains. For example, under mail > add/remove/manage accounts, you will see drop down menus so that you can make email addresses for either the main domain, or newly created addon domain.