Theoretically, you should never need to restart (or kill and relaunch) an iOS app. The operating system manages the lifetime of an application for you. But if you do wish to kill an application, iOS makes it easy to do so.
To restart an application:
- Tap the Home button to get to the Home screen if you're not already there.
- Double-tap the Home button. The app switcher will appear, and you can swipe sideways to navigate through the running apps.
- Find the app you want to kill by scrolling sideways if you don't see it visible.
- Swipe the app upwards off the top of the screen.
The app should disappear. Now you can launch it again, and it will start fresh.