How do I update my monthly Subscription details such as the payment method or billing address?
While you will find your payment method information on your main user account page, under the "Account Settings" tab and "Payment Methods" link, the actual payment method that is tied to your live subscription is to be found in your Subscription details.
So you should go to the "Orders tab", in the "My Subscriptions" link. This is where you will be able to update / edit / add / delete your credit card information, as well as update the billing address information per subscription.