I puchased a new domain, call it xyz.com.  I want it to be a separate domain that is not linked to my present website, zyx,xom.  As I understand the addon domain category in cpanel, if I added xyz.com as an addon domain, I would have to access it via www.xyz.zyx,com.  Is that correct?  If so, how do I go about getting xyz.com to stand alone?

No, this is not correct. An addon domain is, functionally, another domain, but the content for it exists within another domain.

If your main domain is abc.com and you bought def.net, and attached def.net as an addon domain, the content for def.net would be found under a folder in abc.com called 'def'. However when you went to def.net you would not see nor be aware of content from abc.com

Just setup the new domain as an addon domain should do it.  It will add a folder inside your public_html folder (if on cpanel or lpcp)

Make sure that any code / urls does not reference the primary domain.

The addon MAY be available via folder.primary.com however users should be completely unaware you are hosting the domain on the same account as another domain and should have no reason to try using that url.

A rewrite could make folder.primary.com automatically redirect to addon.com

If any issues, such as primary showing up, contact support@lunarpages.com (email) or support.lunarpages.com (web)

OK, so now the new domain, zyx.com, is in a folder zyx within the xyz public_html folder.  Outsiders can reach the new domain by just using www.zyx.com, correct?  As far as content goes, do I put a new index.htm for zyx inside the zyx folder? And that will be reached by an outsider using www.zyx.com?  Is all this correct?

Thanks, I've got it working now. It did show the wrong address, but I fixed it (I'm not sure exactly how I fixed it, but I did  ).  Thanks again for the help.