I followed the answers here but when I tried to connect with my new user, I got an error message stating "The server principal 'newuser' is not able to access the database 'master' under the current security context"
.
I had to also create a new user in the master table to successfully log in with SSMS.
USE [master]
GO
CREATE LOGIN [newuser] WITH PASSWORD=N'blahpw'
GO
CREATE USER [newuser] FOR LOGIN [newuser] WITH DEFAULT_SCHEMA=[dbo]
GO
USE [MyDatabase]
CREATE USER newuser FOR LOGIN newuser WITH DEFAULT_SCHEMA = dbo
GO
EXEC sp_addrolemember N'db_owner', N'newuser'
GO