Please watch the above tutorial first and then read the below (VERY CAREFULLY).
 
1)  Please make sure that any domain you add to your account have the correct name servers. Click Here to
     learn more about name servers.
 

2) When you publish to your new domain name make sure to publish it in its own sub directory

For example; For your main website, you would be publishing to your public_html folder. for your new website. You would publish public_html/site2 folder. You are going to have to manually add /site2
after the public_html in the below publish box.
 

 
3) Make sure to call your new websites homepage "index" If you are not sure how to name your websites
    pages please click here.

4) now if you go to www.site2.com on the internet, you should see the home page for your new website.

5) I have used site2 as an example, you can call it anything you like.