You probably realized that you cannot use the traditional approach of creating logins on Azure hosted SQL Server by right-clicking on "Logins" on SSMS.
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You will have to run the create login scripts manually. Here is how you can do that.
use master
create login <username without quotes> with password = <password enclosed in single quotes>
E.g.
use master
create login myappuser with password = 'StranGeBeast123$'
If you then need to grant this user access to a specific database, then you have to create a user under that database and link it to this login. Here is how you do that
use <your app db>
create user <user without quotes> for login <login without quotes>
E.g.
use myWebAppDB
create user myappuser for login myappuser
Then grant any appropriate roles. In this example below, I have granted db_owner role.
ALTER ROLE [db_owner] ADD MEMBER myappuser
