There are many ways to accomplish this.

The anonymous  user could create a new ListItem that (from simple to more
complex):
* Generates an alert to those that need to know about it (assumes that outbound
email is configured which is likely)
* Triggers an SPListEventReceiver that sends out the email (requires some simple
custom code)
* Triggers a Workflow that creates a task, sending out the email (more complex
but more complete)