There's a well-documented example of an
ASP form-mail script at the
BrainJar site (this resource is also referenced in my "Programming Resources" sticky).
The usual routine for such a script would be for the visitor details to be collected by the form, emailed to the site owner, and the visitor would either receive confirmation on the same "form" page that an email had been sent, or alternatively, they could be redirected to a separate confirmation page. So there's no need to add an additional email to the visitor.