How do you close programs?

I posted another topic about constantly getting "Low Memory" in my status bar. I was under the impression that just doing a long press of the home button, bringing up the apps and swiping them off the screen would close them. Well, I guess not. While driving, I inadvertently swipped Pandora off the screen and it was still running (the song kept playing). I meant to select it to put it on the front of the screen.

One way might be to set my Fast Reboot Pro (a paid app) to reboot when my screen goes off, but I'm not so sure I want to do that.

Is there another way to close apps?