how can I countersign a form and send back to the person I received from?

You can add a condition in the form which specifies that if the required signature field is filled and form submitted, to send the form to the required person. But before that create an email notification to send the form to and create a similar condition as below.

Some useful guides:

https://www.jotform.com/help/25-Setting-up-Email-Notifications

https://www.jotform.com/help/167-How-to-Send-Email-Based-on-User-s-Answer