I wrote about this a while ago in my Joomla microdata article. It has struck me since that it was complete overkill to add authorship in that way and can be done without any code changes at all, just using the standard contacts component.
The reasoning is, that you don't have to link each article on the site to the authors Google+ page. If there is an author page on the site, and each page is linked to the author page then you only need to add the link to the Google+ profile on that author page.
So this is pretty easy to set up in Joomla, but not something that people usually do. The contacts component has always been there, I just don't really know anyone who actually uses it. Joomla 2.5 brought in some changes to the component which actually make it easy to add authorship links, but it won't work automatically, you still need to let Google know you write for the site before it will work.
By default, the 'author name' and 'link author' are enabled in article options globally. That means that, if a user has an associated contact in the contact component, each article written by that user will be linked to the contact page for the author. That's all Google needs to associate those pages with a Google+ profile.
With Joomla 2.5, the contacts component has extra link fields where you can add links of your choice. So it really just needs a link to your Google+ profile with ?rel=author attached to the end of it.
Go into the contacts component. Create a new contact. Add the name exactly as it displays on your Google+ profile. Add the rest of your details and a short description if you wish, then look to the 'display options' tab and scroll down to the 'link a', 'link b' etc area and add the link there. It's a bit of a shame the fields were added in this way and not 1 field with a plus button to add another (could be stored as json quite easily) so you could add as many links as you liked, but I shouldn't complain in retrospect after offering no input and 3 is still a short term release (so maybe I should add a feature request? where? Would be nice to be able to specify link target also...).. In one of the fields add the link to your plus profile with the rel author, mine would be
And that's really it from the Joomla side. It won't work automatically though, it has to be a 2 way thing. Your Google+ profile has to link back to the site to say that you are a contributor to that site for your image to show in search results.
Login to your Google+ account. Click on the profile link in the main menu and then the 'about' tab and scroll down to the links section. Click on edit, and in the 'contributor to' area, add a link to your website (using the correct www/non-www prefix if you have redirects running), save and that's it. Wait a while and then try a Google site search on your site, site:mywebsite.com and check to see if anything shows up. It can take a while depending on how long the site has been around and the profile (I recently moved my old Google+ profile to my current email and site to a new domain and mine has disappeared! The old site was around for a while and images went up in a day.)