Google didn't lifting any stone unturn, to make user get involve with it new social venture, Google Plus.Way back, in october Google give the hint of integrating the blogger profile to Google+ profile. Today Google start the process, user can replace their Blogger profile with Google plus profile.
If one is using the Blogger's new interface or blogger in draft then he may get the message in the blogger dashboard to connect the blogger to Google+. See the pic below.
As you can see, this allow you to connect the Blogger profile to Google plus. Click on get started button, and connect your blogs to Google plus. By doing so you will gain, post sharing on Google plus with your profile image display while you blog article appear in search result. As you start the integration you will see the next image (of-course of your not mine :-)
After that your job is finished and in blogger dashboard you will see the message that "you are using the Google+ profile on blogs".
Thinks that need to consider is that you must keep all the data of blogger profile which will be deleted after 30 days and you can revert back to blogger profile in those 30 days only. So make copy of details of your blogger to Google plus profile.
If you want to revert back to blogger's profile you can do this by clicking on the setting icon on the blogger's dashboard and choose the Revert to Blogger profile option.
Also if you had discarded the the message as shown in first image you can check the same setting icon and choose Connect to Google plus Profile. Or direct link for that is http://www.blogger.com/switch-profile.g so you can access any!!!
Watch the Video below which demo the switching of blogger's profile to Google plus profile.