The payment notification will load a URL, and that would be a script that takes the details and does something with it, e.g. an affiliate tracking software, a custom script… https://s2member.com/kb-article/building-an-api-notification-handler-webhook/
The notification has several replacement codes you can use, including the amount paid. See: WP Admin > s2Member > API / Notifications > Payment Notification
Are you getting other emails sent? If emails are not being sent, see if the tips here help: https://s2member.com/kb-article/troubleshooting-email-delivery-problems/
If other emails work, but that one isn’t going out, maybe the notification is not firing…
Did you verify that you entered the email address correctly in the payment notification configuration?