Google's Author Markup badges?

so whats a Google +Badge?

Google+ Badge is a widget which enables one to easily llink there  Google+ page to there site,to get more recommendations for your site in Google search and grow your audience on Google+.

Because Google+ pages and profiles are different, they offer two slightly different versions of the badge: one for each case. Badges that link to Google+ profiles allow people to easily find you on Google+ and add you to a circle directly from your website. Badges that link to Google+ pages include these features and add some additional functionality. They help Google consolidate +1's from your website and your Google+ page, and make your website eligible for Google+ Direct Connect.

There are 3 ways to display the  Google +Badge

1.Dispaying it in google's direct search

For one to see this they must be already signed into there plus profile.
here one will see the + badge  whenever they hover over the search results as shown below
to achieve this just add the following code just after the head tag

<link href="https://plus.google.com/{plusPageUrl}" rel="publisher" />

where   "plusPageUrl " is your plus page url

2,Page Badge 

The Google+ badge allows visitors to engage with your brand directly from the badge itself. The minimum code required to render a Google+ badge on your website is one JavaScript include and a badge tag.

<script type="text/javascript" src="https://apis.google.com/js/plusone.js"></script>
<g:plus href="https://plus.google.com/{pageId}"></g:plus>

 where   " pageId " is your plus page url

3.Profile badge tag

The Google+ badge allows visitors to engage with you directly from the badge itself. The minimum code required to render a Google+ profile badge on your website is one JavaScript include and a badge tag:

<script type="text/javascript" src="https://apis.google.com/js/plusone.js"></script>
<g:plus href="https://plus.google.com/{profileId}" rel="author"></g:plus>

  where   " profileId  " is your plus profile url

NB:  The {}  only provide a guide to where you put your id and should nevetheless be included in the code.

for more infomation on google plus badge intergration pliz check the comprehensive guide on google.Follow it google plus badge intergration