This article applies to Classic Commerce. (Looking for Contextual Commerce documentation?)
A correctly applied 100% free order typically will not require a credit card. Sometimes the fields will show up in the order process due to a caching issue. In these instances, you should close all browser windows and start with a fresh session.
Some of our page linking options handle a free coupon better than others. For example, Option 5: Shopping Cart - View Product Detail Page asks for a coupon code in the order process after a customer clicks Add to Order. There customers can enter in their coupon code, click Update Coupon, and the price immediately changes to $0. When the customers clicks Order, they are never asked for payment information.
With many of our other order process flows, when customers go through the order process, they are first asked to select their payment method and then they are taken to a screen that with ask for a coupon code and credit card information. When a customer enters in your coupon code and clicks Update Coupon, the credit card fields will disappear.