First, go to Orders > Customers and select the customer you'd like to add a discount to.
Now click Discounts on the left side and enter in your desired discount amount. For example, 10% would be entered as 10.
Be sure to save!
How the Discount Works
Go to your Take Order screen and search for the customer you just edited.
When you enter in a product, you will see that the discount amount is automatically applied.
Now you can process the payment as usual.