It’s seems Google tries to find a silver bullet to split high quality content from shit. The way they chose is to distinguish an author of this or that article. This fact means the text is better than an anonymous staff.
The new way to distinguish the authorship is called Google Authorship. Simply put, you can tell Google “Hey, I am the author of this content”.
There are 2 roles of “authors”: authors and publishers. A site usually usually represents a single publisher, but can have multiple authors. For example, New York Times or developers.org.ua is a publisher. Every article on those resources has its own author.
Both roles are setup via Gooogle+ profile. It’s a must, otherwise nothing works.
There are two and half ways to tell to Google who you are.
Way #1. Email on the same domain
Prove your relation to the website via an email address on the same domain. You can read Google guide on it first.
Way #2.1. A HYPER-link to Google+ profile
Add a usual hyperlink to your Google+ page with “?rel=author” at the end of the URL. Disadvantage is that you need to have a hyper link to an externtal resource which is not always a good idea.
Way #2.2. A link to Google+ profile
Just add a link, not “hyper”, just add this tag anywhere on the page:
<link href="http://plus.google.com/...." rel="author" />>
You can test if your setup worked well with help of Google Structured Data Testing Tool.
Pay attention, that it takes a few days/weeks for that to appear in live search results, and Google says it’s optional. They don’t promise you see your face there, put many people have it worked.
What else can I do?
1. It seems Google shows your pic only if you some kind of a known specialist of the topic, but it worked without that for many other people.
2. Also they advise to claim your authorship only for guest articles, not for articles of your own blog.
3. Another thing to pay attention to is how many circles your Google+ profile is in. The more popular you are the better.
Good luck with it!