When you proceed to payment, make sure to check the box "add a gift card or discount code". You find the box under your selected products. Enter the code on the back of your gift card in the field that pops up. It's important that you enter the code exactly as you received it. Unfortunately, you cannot combine gift cards with discount codes when making a purchase.
You can't add a discount code to an already placed order, or combine multiple discount codes on the same order. It is not possible to apply discount codes to already discounted products.