If you have a discount code, you can follow these steps to claim your discount.

First, visit the company billing page, which is available in the sidebar of your company settings.  See below:

On the billing page, select the upgrade / purchase you wish to make.  Prior to approving payment, you will see a "Review Order" popup.  The coupon code option is located in this window.  

Once you enter the coupon code, you should see the discount apply to your payment today.  Then you are free to complete your checkout!