For existing subscriptions, Norton uses automatic renewal and charges a credit card that is on file within the account. If no card is on file, here are the payment methods that are accepted in United States:
VISA – JCB – DISCOVER – Mastercard – PayPal – American Express

The above payment methods are also used when buying a new Norton subscription.
If you want to update your billing information, including the payment method, check the article about Updating Norton Billing Information.