When on a Nokia Lumia phone, to completely close a program and end it's process, simple press the back arrow button on the bottom left of your phone. When in an app, pressing home returns you to the home screen and allows the app to keep running - but pressing back ends the process. To end all extra processes on your phone, simply keep pressing back (it has an animation, showing you the apps it closes) until you've closed everything and you cannot press back anymore.
Additionally, you can go into Settings, flick left into Applications and select Background Tasks. There, you can see what tasks are running and terminate them.