Go over to Google.com, click on waffle icon up at the top right corner and click on the "@ chat" icon.
After the intro, you will be presented with this new page where you can click on either "+new conversation" or "message" and it will take you to where you can add the email address.
Once the new page pops up, go ahead and hit "send invitation" You can also customize the message that is being sent with the invitation.
You will be directed to the Google Hangout page. Click through the introduction.
In the search bar, you can add my email address "firstname.lastname@example.org" and click on my contact information. Hit enter to be directed to the next step.
... and walaaa! The invitation has been sent and all that you will need to do is wait for me to accept it.