After the person has submitted their survey, can we design an automated email that gets sent to them?

I want people to sign up for our contest online and then receive a customized confirmation email after submitting their form.  

Yes, it's possible to do that, once you add a email field to your form an email auto-responder is generated automatically. 

You can also manually add it to your form and customize it, here's a guide about it: https://www.jotform.com/help/26-Setting-Up-an-Autoresponder-Email 

If you have any question, please let us know.