Hi, need some help please.

I have read that if the search engines pick up different domain names for the same domain, for example:

mysite.com
www.mysite.com
http://www.mysite.com/index.php

then this will be seen as different sites and counted as duplicate content and penalised accordingly ? 

I wonder if this is what has happened to one of my add on domains because if I do a keyword search in Yahoo, the domain name in the results description comes up as mysite.com omitting the www. in the search results description.

Yet if I search by the domain name, for example, mysite the domain comes up as it should www.mysite.com in the result description.

Could the search engines be picking up different domain names and this could be affecting my ranking (because it is ranked badly...I know if could be a million other things but trying to eliminate...and I do not know the first thing about htacess, redirects in CPanel etc...so this could be set very wrongly)

If this is possible can anyone help me and tell me what I need to do, to direct all possibities of domain names to www.mysite.com, so that the search engines see it as one site

Thanks 

My primary domain is ranked very well 

In addition to the link Mitch posted, if you sign on to Google Webmaster Tools and go to Settings you can set your preferred domain name (domain.com or www.domain.com) there.

You add the lines from the link Mitch posted to your .htaccess file (in the public_html directory).  Go to Cpanel, File Manager to edit.

You only need to worry about redirecting the domain name part of the url.  mydomain.com to www.mydomain.com or vice versa depending on which one you want to use. Don't worry about index.html.

I'm not sure what addonone refers to in your example.  If it is an addon domain you want to redirect mydomain.com/addonone to addonone.com.  If it is a subdomain you want to redirect it to addoneone.mydomain.com.  If it is just a directory you don't need to worry about it.