Email copy of form to person who submits it

Is there a way to add an email field that will then email a copy of the form to the person who submits the form for their own record?

Yes, this is possible in JotForm. You need to create an Auto-Responder email. Please check these helpful guides:
Creating-a-Form-Autoresponder
Explanation-of-Email-Notification-and-Autoresponder-Settings

If you have any questions, let us know. Thank you.