how do I know if apps are running in background?

If you have multiple apps running on the multitasker and they are updated to iOS4, these features may be running in the background.
* Fast App Switching
* Background Location (indicated by a white/purple arrow on top)
* Transfer Services (Bank transaction downloads, newsletter updates, etc)

You can install a memory task application and see what apps and tasks run. If you have less than 50MB of "Free" memory remaining, it's running lots of tasks in the background. Lots of tasks equals lots of battery power used.

you dont!!

best bet is to double tap the home buttong (square at the bottom) and then shut down all the apps that are on the button of the screen. hold your finger on an app until it starts to jiggle like it does if you want to move apps on the home page or delete apps.

The only method is to open multitask and the apps listed are the ones running. Apps that have "push notification" ability semi-run in the background but it's mostly server side pings and very little client to server pings when closed.

Home screen apps don't have a green checkbox or other indication to say they are the ones currently running. None of the home screen apps will show you they are running.

The apps available when double-selecting the home button may or may not be "running". Most apps are still quit when selecting the home button to leave the app and this will continue. Some apps will be suspended when leaving the app such as a game, but when such an app is suspended no CPU cycles are being used, and a few apps can or will truly run in the background such a music streaming app, a GPS app, or an app like Skype that has been updated for 4.0 to use one of the multitasking APIs.

http://whenwillapple.com/blog/2010/04/19/iphone-os-4-multitasking-explained-agai n/

http://whenwillapple.com/blog/2010/04/19/iphone-os-4-multitasking-explained-agai n/