I read this article: https://msdn.microsoft.com/en-us/library/azure/ee336235.aspx
I don't know how to connect to the master database. I don't see it anywhere on the portals.
I want to be able to manage which credentials have access to which db and at which level. Preferably using a GUI.
There are a couple of ways to manage credentials in Azure SQL DB.
The simplest is to use the GUI in the NEW azure portal (https://portal.azure.com/) -- open the SQL Database server of interest and manage access using the "Roles" and "Users" options in the "Access" group at the bottom of your Server pane.
You can also connect to the Server using Visual Studio (SQL Server Data Tools add-in). Open Visual Studio and under VIEW, select SQL Server Object Explorer. You can add the Azure DB server to that tree, you will have an option of connecting to the "Master" database (under System Databases) and running SQL commands to create users, or graphically add new users under Master > Security > Users. Once the user is created, logins can be created and then individual database permissions added.