Android, how do you know if an app is running the background?

[Student]

I'm trying to optimize my phone for good battery life, I've had to charge it every day since I got it a few days ago. It's an HTC evo v 4g from Virgin Mobile. Although I've been playing around on it a lot so I'm assuming just the screen takes up about 90% of the battery. It says in the manual to optimize battery life, don't have apps running "in the background" but I'm not sure where to find "the background" other than what's in the top left-hand corner of the task notification bar and also going into settings->apps->running and finding what I'm assuming are critical apps to be currently running like "vdm client," "htc location service," "lookout" (I downloaded this app for phone security), "google services," "media," "maps," "voicemail," and "touch input."

I have widgets on other screens like the cnn top stories and also a twitter widget so I'm assuming the twitter gets periodically updated...and also if I choose an app under app settings, I have the option to "force stop" so that would imply that these apps are already "started"? I have gps and 4g enabled for apps and data.