Is there a standard UX best practice for displaying a message to the user informing them that the email was successfully sent via a form?
Unfortunately not. There are varieties of the ”message sent successfully”, but no standard or convention available. In these cases, where there are no real convention, one can look at the web applications that users are familiar with.
GMail.com by Google uses an information box where you have a link to the recently sent message.
Outlook.com by Microsoft have no information box, but they have implemented an animation which make the user understand that the message was sent. Both these services implement different techniques – but the intention is the same – let the user know the intended action worked.
There are two things to consider here.
It’s important to let the user know that the message was sent, but one need to make sure that the message actually was sent. There are few things in User Experience than to convey a message that is wrong. Telling the user the message was sent when it actually wasn’t is equally bad as telling the user the message wasn’t sent when it was. Make sure the right message/animation is in place.
Let the user have a way to see the sent messages (if applicable). If you’re implementing a financial or insurance app, users should have a way to see their previous sent messages. But if this is a support web for a device you’re selling, that may not be as important. Either way, consider whether or not to have a sent message view.