You can enter the coupon code on the My Cart page as shown in the picture below.
If the box does not appear it may be that your purchase cannot be discounted. If you are purchasing overweight or oversized items that are not available for home delivery you also may not be able to use a coupon. Certain other product categories or types are not eligible for further discounts. If you are still having issues try calling 1(800)AUTOZONE (1-800-288-6966).