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Go to Web administration http://www.<yourdomain>/admin on the hosting service, or to http://www.thehostingcontroller.com/admin

Login with your web admin account.

Click the menu button on left for Domains | List Websites

Select the existing web site's domain (e.g. mydomain.com) and click the button on the right for Properties.
 
Click Host Headers button on right.

In pop up window, typed www and the new domain (e.g myaliasdomain.com) and click Add. Again in pop up window, left blank field and type effective-communications.org and click Add. Close the pop up.
 
Click menu button on left for DNS Manager | List Zones.
See that the new domain is listed and points to the same IP as the existing site.
 
You will of course, depending on how you registered the new domain name, you will either want to get your domain registrar to point to our DNS servers at:
ns1.thehostingservice.com 209.47.166.24
ns2.thehostingservice.com 209.47.166.3
or else change edit the 'zone' files of an existing DNS server to
point the new domain (with and without www hostname)
to the IP number of the new site.