First thing to do is go to your google plus account, if you don’t have one, you have to get one for this to work.
Next put a link on your webpage or blog that has this:
<a href=”http://yourwebsite.com/author-bio/” rel=”author”>Author Name</a>
into your webpage.
This notifies google that you are the author, and also verifies this to your google plus account. After this go to your plus account and make sure that you have your website listed under “contributor to” section in your google plus page. Then, after that you should be good to go. It may take some time for your new posts to be updated, or for the change to take a place in your google search results, but that should do the trick after Google updates.
Also, in the posts that you post in the future, be sure to have some where on your post (one you want to be listed in search) have by YoUr Name So that google will update the search with your G+ image and name.