Eventually, a project makes it to End Game.. as we call it.
#1). You'll need an "A Record" in DNS.. pointing to your azure deployment url's IP. This will make your site.. resolve to the IP address for your load balancer.
#2) You'll need to make a CName record, for "www". So that www.yourdomaingoeshere.com will resolve for your customers. Use your azure production deployment URL.
#3), You'll need to get your https certificate. Make sure to import it, with the private key.. and then export it back out. Upload that cert to your azure deployment. Attach it in your project via the screen shots above.. by right clicking on your web role.
Very quickly, you'll realize: Cloud work is just like regular development. There isn't any magic here.