Is there a way to let the "person who filled out the form" print the completed form after submission?

You can add the print button to the form as explained on this guide: http://www.jotform.com/help/24-Print-Button-on-Forms

So, the person can Hit the print button before submitting:

Let's say the person hits "Submit" before printing the form, creating an email autoresponder is the solution: http://www.jotform.com/help/26-Creating-a-Form-Autoresponder

Make sure to add the edit link of the form while creating the autoresponder:

In that way the person will get the email, with the already filled data, and will be able to click the link to hit the "Print" button.

If you need anything else, please open a new thread, we will be glad to assist you.