A discount can be applied to any order that is pending payment. The discount reduces what the purchaser owes, and they pay the rest. To find pending orders, go to the orders search list, select the Pending Payment status, and click the order number to view its details.
From the Actions menu, choose Add Discount/Financial Aid.... In the window that opens, choose one of:
Enter a reason for the discount, then click Apply Discount. The order now shows its subtotal, a Discount/Scholarship/Financial Aid line, and the new, lower total.
Only site admins, staff members, and store managers can apply a discount, and you can't apply a discount to an order you placed yourself.