Log into the server, where your PrestaShop is installed (eg through FTP) and locate the file:

[prestashop_dir]/webservice/dispatcher.php

In the first lines of the file there will be a code:

require_once(dirname(__FILE__).'/../config/config.inc.php');

Add the following line before the above line:

define('_PS_MODE_DEV_', true);

Here's how it looks after the above change: