To update the billing or payment information on your Grizzly.com account, start by logging in with your username and password. Once you're logged in, go to the "My Saved Payments" section, where you can easily manage your payment methods. Here, you can update details like your credit card's expiration date or billing address. If you need to change your entire credit card number, such as when you get a new card, you'll need to remove the old payment method first. After that, you can add your new card by entering the full card number and other necessary details to keep your payments running smoothly.