Summary
From Fieldwork you can tell by the Stripe Reference # in the payment.
The reference number is also in Reports > Income.
Key Points
Log in to your Stripe account to verify payments
Download the Stripe app to easily access your account
Log in to Stripe to check payment status and reason for a decline
You can verify a payment through Stripe by logging in to your Stripe account and checking the payments there. Stripe also has a mobile app that can alert you to incoming payments.
If the customer's card is declined for an unknown reason:
Log in to your Stripe account http://www.stripe.com/
Look up the customer by their email address
Look at the transaction, the status and a reason for the decline