I'm never sure if they close just by going back to the home screen?
Hold the home button as suggested, until the apps appear, don't just tap it once.
When I hit the home button, all the icons come up. I was told that I have to go to manage apps, then go to running apps, and click on the ones i don't want and then hit stop. Seems like a pain, since I'm not sure which apps are ok to close.