What would be the easiest way to convert a web app to use single sign-on?

That is, I need the user to be able to browse to the app page and the app would open a database connection using the user's credentials without having to type username/password.

It currently uses a custom authentication method that requires username/password and the app uses its own database credentials.

Would it be better to start using services.addIdentity() ?

Whatever the solution, would that still be applicable if the web app resides on an Azure server?