How do you plan to process the credit cards?
The easiest thing to do is to purchase one of the add-on payment gateways that support credit cards: http://easydigitaldownloads.com/extensions/
There are several of the gateways that include credit card support:
- PayPal Pro
If you want to add the fields manually, then checkout the developer's API section that describes the hooks available on the checkout page: http://easydigitaldownloads.com/docs/section/checkout-page/
You will have to be at least a little bit comfortable with PHP to add the fields, but it's really quite simple.
I also have a tutorial on adding custom checkout fields: http://easydigitaldownloads.com/docs/custom-checkout-fields/