There are two different ways to share items from your RSS subscriptions in GoogleReader with your circles in Google+. One allows you to share privately, the other is a public share. Neither is as straightforward as shares once were in GoogleReader.
First, the public share, where “public” means that the shared item will show on your Google+ profile, +1 tab.. ["Your +1's appear here. +1 the things around the web you like, agree with, or want to recommend to others."]
At the bottom of any RSS article, there is a footer with +1 and email buttons. First you must +1 the article. When you do so, you’ll be prompted to share the article with Google+. When you click inside the “Share on Google+” box, it will expand to provide you with room for a comment, a preview of the article, and a way to select circles or individuals with whom to share. This looks like a truncated version of the Google+ share interface.
Note that you can only share this way with people who have GoogleProfiles!If you want to share the article with someone who is not on Google+, you’ll need to resort to the email option.
But what if you don’t want an item to show on your +1 page?
Then you should click the “Share” link in the upper right of the black task bar. That will launch a pane in the notifications space. Ironically, it contains the same “photo, YouTube, link” widgets that a Google+ post has … but in this case they are grayed out because, well, you are sharing a link!