You can take payments on your custom forms, event tickets, donations and products. To take payments, you will need a payment processor (WePay, PayPal, Braintree). These can be added under Site and then Payments.
Duplie does not store the credit cards. We let the payment processor to all that for us. Duplie does integrate with the payment processors to allow for a recurring payments (donations) and remembering the users credit card (if they choose).