Regardless of what you think of Google+ as a social network, it continues to grow and is very popular with some users. Many websites have offered the Google +1 button for a long time. In fact, we've had the Google +1 button here at SlashGear for a long time now. That button is more like Facebook's Like than anything else since it simply gives the ability for users to endorse a story on Google+.
However, I would bet many times people read stories they find interesting and would rather actually share the story to their Google+ friends rather than simply giving it the old +1. Google has announced that it has made that possible with the addition of the new Google+ Share button. The way Google has pulled off the new share button reminds me a lot of how likes for Facebook works.
When the user goes to the page that has the new share button it will show how many people have shared that story and include friends who are in their circles who have shared it. The button starts off white if the user hasn't shared the story, and after they click it to share with friends, the button turns red. You should start seeing the new Google+ Share button pop up everywhere because it is available globally as of now.