There are two ways to accomplish this.
If you just want the new domain to forward (redirect) to your existing domain, log in to your cPanel and click "Aliases" in the "Domains" section (please note on older cPanel themes this icon may say "Parked Domains"):
Enter your domain name and click "Add Domain":
You'll then be able to configure where the domain redirects to.
If you want the new domain to function as a separate site with separate content, log in to your cPanel and click "Addon Domains" in the "Domains" section:
Enter your domain name - the "Subdomain" and "Document Root" fields will be filled automatically. If you wish, you can create a new FTP user by checking the box "Create an FTP account associated with this Addon domain". Enter the desired username and password and click "Add Domain":
Please open a support ticket if you need any further assistance.