Suppose you want to enable one database connection plus zero or more social and enterprise. In that case, it’s straightforward: you would have a prompt for the username and password for the database connection and buttons for the rest on the New Universal Login Page.
If you want to enable more than 1 database connection for an app, then you need to specify the connection parameter in the /authorize request (Auth0 will not filter your database connections to choose a relevant one for the user).
There is also a Home Realm Discovery for enterprise connections → meaning if a user enters an email that matches the domain set for the enterprise connection, the password prompt will be disabled and the user will be redirected to the enterprise login page.