How to enable Save form and continue later on our form?

what widget or feature do I need to add to allow information that is entered to save when someone submits a form and the payment method declines or the form restarts

I am not sure if I understood your question well. You want a feature or widget that will allow data to be saved on submit.  What is not clear however is "and the payment method declines or the form restarts" but I will assume you want user to re-fill the form with their previous data such that they do not start again from the beginning in case Payment is declined.

If this is the case then you can take advantage of the "Save form and continue later" feature we have. Below is a guide on how you can enable this feature on your form.

https://www.jotform.com/help/97-How-to-Save-Forms-and-Continue-Later

If the above does not resolve the issue raised we will kindly seek further clarification on the issue raised.

That is not, what I was wanting to happen is if someone fills out the form and they submit the payment and it declines the form restarts is there anyway for the user to fill out the form and have the entries saved to add a different payment method if the one that was supplied declines

Unfortunately there is no option on checking if payment was declined and redirecting it back for the user to fill it again. This is because payments are not handled by Jotform but rather the payment merchant.

Once payment is successful or denied the payment merchant redirects back to the form with a new session.

The only other option is you can redirect your form to a thank you page upon submission and you can ask users to check email to edit their submission if their payment was declined. This will mean then that you will set the "Save and continue later" feature as shared earlier.