how to get author image in google search results

Google authorship programme 

Google Authorship helps authors establish authority on SERPs through the content they write

First of all, below points are to be compulsory

• A your own blog or website
• A Google Plus Account
• An About Me page on your blog.

if "about page" is already present in existing site or blog then need not to be worry but author link should be present there

if you made above points succesfully , then follow below steps
On your website or blog add this link,

<a href="https://plus.google.com/GOOGLE+ ID"
  rel="author" target="_blank"> follow me on Google+</a>

1) Replace GOOGLE+ ID with your Google plus id. You can get your Google Plus ID by going to your Google Plus profile page

2) Next go to your About Me page and add this link anywhere you want,

<a href="https://plus.google.com/GOOGLE+ ID"

  rel="me" target="_blank"> My Google plus profile</a>

3) Now go to your G+ profile and click the “Edit Profile” button

     Then click on the "LINKS"

     Add your Blog/site homepage URL and also the URL of your About page.

4) Finally Save your profile and you are almost done.  

lastly check this link to verified if it done properly

http://www.google.com/webmasters/tools/richsnippets

it will shown like this

@ seo freelancer