My answer will reflect the specificity of your "question." You need to create to a user plugin and listen to the onContentPrepareForm event so you can inject your custom fields, making sure the context is com_users.registration. Then u need to hook into the onUserAfterSave or onUserBeforeSave event to capture the entered data and save.
A point of caution, I highly recommend you do not save customer credit card data in your Joomla database. You are exposing yourself and your customers to unnecessary liabilities in addition to a whole host of regulatory requirements when dealing with financial data.
If you do not simply transfer the client credit card data to your 3rd party payment platform and save a customer reference number for later access, you need to seriously reconsider the vendor you're using!
Joomla Plugin Events