When checking out, you will go to paypal.com right away, this is where PayPal collects your shipping and billing addresses. After entering that data, you will return to Shopify where you will see your shipping rate; this is where you type in a discount code (where it says PROMO code) and your price is updated according to your code. On that same page, your will get to apply your code and finalize your transaction.
***NOTE: If we have a large sale going on, we disable the use of discount codes to prevent double discounts. So there is high chance that discount codes will NOT work during a large sale***