Opting a customer out is just a DELETE HTTPS request against the Contact resource URI. You would use similar code to this post, just change the request type to DELETE and don't send any content (DELETE request do not need content sent).
Nice, so I figured out how to do the Delete; however, it requires me to get the Contact ID of the contact I need to delete. Is there a call that I can make if all I know is the person's email address to get the Contact ID?
That would require a GET request using the format described in our Searching for a Contact by Email Address documentation.