I installed the free version of the Nova Launcher about a week ago and it worked like a charm. But sometime later, after I close an app, the default TouchWiz UI appears instead of Nova. I usually open an app and close it again so that I get the Nova Launcher. I am using a Galaxy S4
Try going under apps in the settings. Find the touchwiz launcher in the list. There should be an option to clear defaults. This should fix your problem. If the problem persists, try reinstalling Nova.