By default, when you click on an RSS feed icon, Opera displays feed contents in some basic format and allows you to subscribe to it with either the built-in reader or some of the popular ones.
But with the recent end of life of Google Reader many will switch to other, less popular readers, or perhaps even install one on their own server.
To add a feed reader to Opera's default reader list, edit feedreaders.ini in "Program Files\Opera\defaults" folder. The format is obvious. There doesn't seem to be an option for a per-user feed reader list.
For instance, if you're using Tiny Tiny RSS, the subscription URL is per faq:
http://your.domain.com/path-to-ttrss/public.php?op=subscribe&feed_url=%s
The code to add to feedreaders.ini will be:
[TinyRSS] ID=20 URL=http://your.domain.com/path-to-ttrss/public.php?op=subscribe&feed_url=%s