How can I make sure I've quit a specific app? As far as I know, some apps quit by pressing the Back button while on the main screen of that app; and some quit by pressing the Menu button and selecting Quit. Should I always first check the Menu button? How can I make sure that I have quit a specific application? I don't want my battery drained by unquit apps running in the background without my knowledge.

By the way, I'm on HTC HD2 with Android 2.2.
That's the thing about the Android OS. A "quit" or "exit" button is not really necessary.  Why? Because the operating system automatically kills applications that are no longer used. For this same reason, there is no need to install a task killer or similar. When you're done with an application, the OS will clean things up for you so you don't have to worry about it.