If you process credit cards through PayPal, you do not have direct access to your customer's credit card details.
If you process credit cards through your own merchant account, you can view your cutomer's credit card details by going to the 'customers' menu and choosing 'orders'. Then select the transaction that you want to view and click 'edit'. For security reasons, only half of the credit card number is stored in the database. The other half is emailed to you immediately after an order has been placed.