If you have correctly applied a promo code or gift card to your order, you will see this in 2 places on the order checkout screen:
The grey box under "Promo code or Gift card" will say that the promo has been applied to your cart.
The Payment breakdown section of your cart will have a line item for the promo code or gift card that you applied. It will state the exact promo code that was applied and the amount that you saved by using the promo code.
If you do not see the discount amount reflected in your order subtotal, then the promo code was not successfully applied.