Well there certainly are a lot of user interface changes in iOS 7 and this is one of them.
In general you really shouldn't need to shut down the running application but sometimes it helps to restart the application if it isn't working quite right. The trick here is to note you need to double click the start button and then once you do that you get a display of all the running applications. You can zoom through them to switch to another running application or ... here's the trick! Just flick with your finger to remove a running application.
So you double-click and then flick. And if you're really coordinated you conflict with multiple fingers to quit multiple running applications.
User interface features that require you to double click before you can use them aren't terribly discoverable. So just think on your iPhone to quit a running application or to multitask double-click that start button i