In iOS 6 and below I could double tap the home button, tap and hold an app, and click the red - to close an application(s).
In iOS 7 this does not work. How can I restart an app that's exploding without resetting the entire OS?
In iOS 7:
An alternative method: (if you're still in the app)
Double tap the home button.
You then get snapshots of the apps that you can scroll to left or right to find the app you want.
You can drag that app up to close it and remove from the display.