First way:
*This is very easy just go to your blog then go to design and then click add a gadget then simply add Google + badge and save it. place it where you want.
Note: Use first method if you are using one Gmail account for both blogger and for Google +. If you are using tow separate ID then you should try second method.
Second way:
*Go to Developer and get a Google + badge for your site to get a badge just enter your google+ profile ID that look like this 117531917611672578844, copy this and paste it into the box given and it will show you a preview of your badges, select one and then copy the code and paste this code into your site or blog where you want to show this badges.
*Now go to your google+ profile page then click edit then go to “Other profiles” and then click add a custom link button enter your site name and site or blog URL then click save.
Now you have to check your authorship is verified or not for this go to Rich Snippet Tool and enter your blog or site URL or any page URL and click preview then you will get the Google search preview if it’s ok you will see a green message saying “Verified” As shown below.
But note that google doesn’t give guarantee to put your information and photo in the search result whether it is verified or not.