To redeem your discount / coupon code, you should find a box at the Checkout page with the label "Gift Card or Discount Code". By pressing "Apply", your discount code will be applied to your cart.
Please note that depending on the device you are using to navigate the site, this discount code box might be displaying differently.
If you are navigating the site from a mobile device, you should tap on "Show order summary" to expand the section where the discount box is contained.