I want to change the payment type on the checkout page to Credit Card. My client does not use a payment gateway, they manually process credit card details. After the checkout page there will be a page for capturing the credit card details.
How do I modify the module to indicate a different payment type?
You'd need to create your own payment module, extending the Payment class.
So I guess you'd define $db members for the card details, getPaymentFormFields returns the card details form that the purchaser completes, and the controller validates & stores the card details.
Bear in mind that if payment card details are being entered & stored on a web server, the server probably needs to be audited by an independent security firm. That's why everyone's switching to payment forms hosted by the card payment gateways.