You can update your subscription’s payment method on Chatbooks.com. First, be sure you're logged into your account. Then, navigate to your Bookshelf by clicking on your User Profile > Bookshelf.

From the Bookshelf, click into the subscription you want to update the payment method on.

On this page, you'll see a settings wheel in the upper right-hand corner:

Click there, and click "Payment."

From here, you can click "Add Card" and follow the prompts there to add a new payment method.

Once it's added, be sure the new payment method is selected, and click "Done."

To learn how to update this on the Chatbooks app, see here.