Within Prestashop you can create "Discount Vouchers" and specify what action you want to happen when a user enters a valid voucher code.
1. Go to BackOffice>>Payment>>Discounts
The following screen is displayed.

This will list all vouchers you have created for your store. The discounts options belwo the list will allow you to enable or disable all discount vouchers
clcik the "Add new"

Code: Enter a code or clcik the "new icon" which will generate a code automatically for you
Type: From the dropdown list choose "Disocunt on Order %", "Discount on Order amount" or "free shipping".
Value: If you have chosen % from the type options dropdown, entrr the percentge amount here, if you chose amount enter the monetary value here.
Total Quantity: How many times is this voucher to be used, irrespectibe of customer
Qty per each user: Now enter the maximun times a single customer can use this voucher code
Minimum amount: What is the minimum order value to be able to use this voucher (If there is no minimum amount leave the field blank)
To be used by: ?
From: Enter the start date this voucher can be used from
To: Enter the end (finish) date after whcih time the voucher will no longer work
Status: Enabled or disabled (When diasbled the voucher code will not work)
When you have completed all fields for your voucher, press save.