No matter what side of the debate you stand on when it comes to clearing out apps in the app drawer on iOS, you may find yourself wanting to clear out or force close apps in iOS 7's "app drawer" but quickly realize it (like everything else) has changed. It's not completely clear how to close apps on iOS 7, but it's incredibly easy.
The first thing you'll notice if you didn't catch the original demo of multitasking on iOS 7 is that double-clicking the home button no longer reveals a drawer with app icons. Instead you'll find cards, similar to what was once found on WebOS, containing a screenshot of the app with the app icon just below it.
You'll be able to swipe in either direction between the cards. Swiping all the way to the right will take you to a card for the home screen, while going to the left will reveal apps that have recently been used.
Tapping on any card will then launch the respective app and take to you to the screen represented in the card. Clicking the home button again won't return you to the home screen, instead you'll be taken to the app you were in when you launched the fast app switching view.
To force close an app due to freezing or troubleshooting various issues, launch into multitasking and swipe up on the app's card -- not the icon -- but the card itself.
The two big takeaways here are: remember to swipe up, and pressing the home button when viewing cards will always take you back to the app you were in, not the home screen.