Once logged in, head over to your profile, click on "My Logins", and then click on "Add login"
It'll take you to the openID login page, select Stack Exchange, and create a new Stack Exchange openID from there.
What then? If I normally create an account in Stack Exchange page, will the credentials from my unregistered account be automatically added to this new registered account using the browser cookie?
You don't have an unregistered account. If you did, and if your browser cookies were present, your unregistered account would be merged with your new registered account