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.
In order to add new user to existin database in windows azure you have to do the following:
First you need to create new login on MASTER database using the following command
I it important to verify what database is currently selected, the next step on creating user in 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 created login, using the following command
Now you need to switch database to your database where you want to add user, it is not MASTER database anymore
CREATE USER MyNewDbUser
FOR LOGIN MyNewDbUser
And the last step is add permissions for the database
Your database again.
EXEC sp_addrolemember N'db_owner', N'MyNewDbUser'