Disclaimer: My experience with Azure, AWS and pretty much every cloud hosted service thus far tells me this post could become dated very quickly so this post should serve simply as a moment in time brain dump.
When rebuilding my homelab environment recently, I went through these steps again and thought others may find it useful so I documented to share my steps. In my scenario, I have MSDN credits for Azure, I opted not to use Active Directory Federation Services, if implanting for an organization, you may want to do that. I just wanted to sync my on premises active directory users and groups into Azure and use my existing domain. The steps were very easy.