How do I create a new site on the same host as my original site?

I am a real new guy in building web sites. In fact this is my first. I run a mac. Now, I have a web site that was prof. built. Works great, done with wordpress. I want to build another site with a different domain on the same server (websitesource.com). I also have two other domain names for the new site which are forwarded to the new site name. I have the new site domain name on the server at ws but have no idea how to upload the new site to it when I get it built. Also should I use a new copy of wordpress or will the one on my original site work ok? Thanks,
Errol