If you are on Desktop you will see a bar or form space that reads "Gift card or Discount code" on the right panel of your checkout screen. You will see an "Apply" button. Click "Apply" and if you are using an active discount code that has not expired and that applies to the items that qualify for that discount, you will see your total price adjusted immediately before you confirm purchase.
If you are on a Mobile device at checkout, on top of the page you will Click "Show Order Summary" to reveal the drop down feature that allows you to enter the discount code and click "Apply". If you are on the payment page on a mobile device, you will see "add a discount code or gift card" where you can click and insert the discount code.