Q: Closing background apps under ios 7

Double tap on the home button and swipe upwards on the thumbnail of the app to close.

You can close 2 apps at a time this way.

Note that very few apps actually "run in the backgroud" (i.e. audio streaming and nav apps). The vast majority are suspended for rapid task switching and don't consume any phone resources.  There's no need to close them unless malfunctioning or actually running

iOS: Understanding multitasking