How do I automatically send a message by email when a customer performs an action on the site?
Visit Admin > Site Info > Site Configuration and go to Common Store Options, where you can find the fields in the screenshot below.

- Site Message for New Registrations - drop-down list, you can select the message name of the message that you want to be sent when a customer signs up on your site.
- Site Message for New Orders - drop-down list, you can select the message name of the message that you want to be sent when a customer purchases an order.
Note!
For the email to be sent, the new customer has to register at the front-end of the site.. Tip!
For information on setting up site messages, refer to the Knowledge Base article - How do I set up site messages?. Direct link to this Question: