When you created your SQL Azure database you were required to provide the name of an Admin user and its password. You can then use your Admin user to run PowerShell scripts involving SQL Azure database as shown below:
# The data center and resource name for your resources
$resourcegroupname = "myResourceGroup"
$location = "WestEurope"
# The logical server name: Use a random value or replace with your own value (do not capitalize)
$servername = "server-$(Get-Random)"
# Set an admin login and password for your database
# The login information for the server
$adminlogin = "ServerAdmin"
$password = "ChangeYourAdminPassword1"
# The ip address range that you want to allow to access your server - change as appropriate
$startip = "0.0.0.0"
$endip = "0.0.0.0"
# The database name
$databasename = "mySampleDatabase"
To create SQL Database users using PowerShell, please read this article.