External web application database calls and authentication

How is the authentication and database calls typically handled in an external application.  I've created an internal application using windows authentication.  The database calls are not a problem because the databases are all located in my company's  internal network.   I'm assuming I would have to create user logins in a database to allow access to an external web application.  I'm not sure about how to handle the database calls.  I would like to have the internal sql database updated from the external web application.  Do I install SQL server on the same external server as the external web application and find a way to replicate the data to the internal databases?  Or should I have the external web application call internal web services to update the internal sql databases?  Any ideas or samples of the best approach for this would help.  Thanks.