How can I tell what is running on the back ground and how can I kill all those background application, how to I quit / shutdown everything that don't need to be running....
To see what is running, go to Menu->Manage apps->Running.
If an app is giving you problems, you can force it to close in this area. However, with more recent versions of Android (say, 2.1 and higher), there is little need to kill all running apps or to use any sort of third-party memory or app management programs. Android will handle that all for you. In fact, the first question most developers will ask when a mysterious bug is reported is, "Do you have a task killer running?" If so, they'll ask you to stop the task killer, reboot the phone, and try to replicate the bug without it running.