To receive emails in a Rails app using Postmark's inbound email processing, one needs to set up a Postmark account and configure it to forward incoming emails to a specific server. This server must be configured with an inbound email address that can be used to identify which articles a response should be associated with. The article ID is added to the email address by appending a '+' symbol. A Rails app must then create a controller method, such as `create`, to handle the incoming webhook payloads sent by Postmark. This method parses the JSON payload, extracts the article ID and user information, creates a new response record in the database, and returns a 200 response code. The `create` method must be configured to disable CSRF protection on the webhook endpoint. A route must also be set up for the controller action. Once all these steps are completed, the Rails app can receive and process incoming email responses from users.