Form Question: Preventing Redirect

We are working on implementing a form on a site footer for email signups. As part of this, we would like to keep them on the page where they signed up instead of redirecting them. 

From what I can tell, a form submission either sends a submitter to the default confirmation/processing page (A green checkmark on an otherwise blank webpage) or, sends the submitter to a landing page or external webpage of our choice. 

How do we instead show a message or a popup thanking them for their submission without moving them to a new page?

Thanks for your time!