Does anyone know how to get your Google+ profile displayed in the right hand sidebar of the Google search results page? As in the screenshot below:
To have a business page appear on the right hand side of google search results page, you will need to have a google plus verified business page, which is symbolized by that small "v" next to the business name. To do such, you will need to have a google plus business page verified by requesting it via this form: http://support.google.com/plus/bin/request.py?hl=en&contact_type=page_verification&rd=1
Jack Lockyer's answer works for displaying a thumbnail image of your Google plus profile on search results UNDER the website title on the left side of the results, as seen here. And by that giant red arrow on your question, that's not what you were looking for. That answer is incorrect.
P.s.: I have done the verification myself for my business, and after less than a week, it was being displayed on search results.
You will need to associate your Google Plus account with the webpage that you're searching for.
In you Google Plus account add the website in the 'contributor' section of your profile, then add the following tag to the header of your webpage:
Wait a few days for Google to reindex your site and you should be away! Ofcourse doing this doesn't guarantee that Google will include your profile in the search results.