To close down apps that are running in the background of your iPhone to speed it up or save the battery charge, press the home button quickly two times. This will make a popup menu appear that displays all the apps that are currently running on your iPhone. On some iPhones, only four at a time will show up on the screen, so you have to scroll to the right to continue displaying all the apps.
In order to turn the apps off from the popup screen, press on the app icon until a red circle with a minus sign shows up. Then, tap the minus sign and that will shut the app down. When you are finished closing the apps that you want to turn off, press Home to get back to your main screen.
Resource iMacify