It's pretty easy. This worked for me...in terms of getting an Azure SQL database down onto your local machine...:
- Open your SQL Management Studio and connect to your Azure SQL Server.
- Select the database you would like to get down onto your local machine, and right-click...select "Generate Scripts". Follow the prompts...
BUT, be careful in that if you ALSO want the DATA, as well as the scripts, be sure to check the Advanced Options before beginning the generating...scroll down to "Types of data to script", and make sure you have "Schema and data"...or whatever is appropriate for you.
It will give you a nice SQL script file which can then be run on your local machine and it will create the database as well as populate it with all the data.
Bare in mind that in my case, I have no FK or other constraints...also, it wasn't a lot of data.
I don't recommend this as a backup mechanism in general...