Payments2Us integrates with a Payment Gateway. The Payment Gateway is what validates and charges a card. The success/response is recorded back in Salesforce (1).
For some gateways, such as Windcave, you need to get card types as Amex or Diners setup as a separate Merchant Facility. Contact support@payments2us.com if using Windcave payment gateway only.
For all other Payment Gateways, you'll need to contact the payment gateway provider directly. Provide them the date/time, amount, card holder name and transaction references (2). They will be able to provide you with a reason of why the card was declined.