Windows Azure user management is a little bit complicated, and unfortunately, there is no way to add users to existing database using Windows Azure management portal.
To add a new user to existing database in windows azure you have to do the following:
First, you need to create a new login on MASTER database using the following command
It is important to verify what database is currently selected, the next step in creating a user in the Azure database should be done on MASTER database
CREATE LOGIN MyNewDbUser
WITH PASSWORD = 'P@ssw0rd'
Then you have to create User on your database using previously established login, using the following command
Now you need to switch database to your database where you want to add a user. It is not MASTER database anymore
CREATE USER MyNewDbUser
FOR LOGIN MyNewDbUser
And the last step is to add permissions for the database
Now switch to your database again.
EXEC sp_addrolemember N'db_owner', N'MyNewDbUser'
How to create new database login in Microsoft Azure (Video)