We have created a Joomla plugin that will help you easily link Google plus profile with Joomla Blogs or articles. All you have to do is install the plugin from Joomla plugin page and follow the basic steps as mentioned on the page. Some of the important steps are:
1.First of all you will need a Google+ profile. If you don't have one this is a good time to create one!
2.Then while you are setting up Contact profile in Joomla, ensure that you enter correct Google+ profile url in Web URL field as displayed in below image
3.Do add link of your site under "Contributor to" section of Google+ profile (under edit profile) as displayed in below image
4.After you have done all this, and enabled the plugin. You can immediately test whether integration with Google+ and Google Search is working or not by going to http://www.google.com/webmasters/tools/richsnippets Enter the url of your page and if the result shows image of the author as displayed below, then the integration is working just fine.
Now it is just a matter of time before your image starts appearing on Google search. Some times you may need to add a new Article / blog to your site so that google can crawl the site for the search index to get updated and new results to start showing up.