How do I finish setting up Stripe to accept payments? Do I need to add the Stripe "secret API key" somewhere?

All you need to do is to connect with your Stripe account, and make sure that it is in live mode:

Please check this guide to learn how to set it up: https://www.jotform.com/help/190-How-to-Integrate-Stripe-with-your-Form 

Let us know if you have more questions.

I believe this part has been completed.  I am connected to Stripe and have successfully processed a test form and payment.  However, a client is unable to process a "live" payment.  When I spoke to Stripe, they mentioned that I probably needed to add an API key to my JotForm account.  

Please note that payments that were made while your integration was in Test mode will not be charged. So, you will need to set your Stripe integration to Live mode, if you want to start processing real payments:

Yes!  This appears to be the missing piece.  Thank you!