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
CREATE LOGIN MyNewDbUser WITH PASSWORD = 'P@ssw0rd' GO
Then you have to create User on your database using previously established login, and add permissions for the database using the following command
CREATE USER MyNewDbUser FOR LOGIN MyNewDbUser GO EXEC sp_addrolemember N'db_owner', N'MyNewDbUser' GO