The Sauce extension for Arquillian Drone simplifies the integration testing of Java EE applications using Arquillian, a tool that greatly simplifies the integration testing of Java EE applications. To use the extension, include the required dependency in your Maven pom.xml file and add specific properties to your arquillian.xml file, such as your Sauce username and browser type. This allows for easy configuration of the Java EE container and WebDriver/Selenium settings, resulting in less code and a more centralized location for these configurations.