By default, the software does not store customer credit card information. This is almost never required anymore when using a live payment gateway, and we STRONGLY recommend against it. The only time this information should need to be saved is if store admins are processing payment through a manual terminal, or when using recurring products (even then, gateway recurring billing may remove the need for this depending on the gateway you are using).
If you decide to save CC information, simply set the StoreCCInDB AppConfig to true.
Viewing CC Information
Full CC information is only visible on the Billing tab, under Orders → View/Manage Orders:
NOTE: That information will only appear to admin accounts that have "Can View Credit Card #s:" checked. Check this by looking up the account under Customers → View/Edit Customers and Users.
Customer Options
VISA PA-DSS requirements state that customers must be able to decline to store their CC information. In accordance with that rule, if StoreCCInDB is set to true, account.aspx will show a "Store My Credit Card Info" checkbox. If customers uncheck that and update their account information, their CC info will not be stored.