Adding WWW before domain name

Best practice is to use htaccess to force all pages to one version or the other.

To force "www" on all pages:

RewriteEngine On
RewriteCond %{HTTP_HOST} ^your-site.com [NC]
RewriteRule ^(.*)$ http://www.your-site.com/$1 [L,R=301]

To force non-www on all pages:

RewriteEngine On
RewriteCond %{HTTP_HOST} !^your-site.com$ [NC]
RewriteRule ^(.*)$ http://your-site.com/$1 [L,R=301]

The .htaccess file should be in the root directory of your website's public_html folder. Also, you may need to change your settings to view "hidden" files on your server in order to see it. (HINT: save a copy of it to revert back to in case you mess it up some how when editing it.)

Once everyone is being forced to one version all authority from incoming links should flow through. Also, over the coming days Google should update all your SERP listings to show the correct version of each page. You can also specify the www or non-www in your Google Webmaster Tools profile for this website & that usually speeds up the process of getting them updated.

I wouldn't worry about which version of each page existing external links pointing to you are using, but for future link building I would encourage others to link using the correct prefix.

Having www or non-www has nothing to do with rankings and is purely your own choice and comfort. But whatever you use stick to the one version and do 301 redirect for the other.