Every once in a while I find myself with an app on my iPhone that is misbehaving. I used to shut the whole phone and start it up again (by holding down the sleep button at the top of the phone until the slide to power off strip came up and sliding it to the right to power down the iPhone). You might also want to shut down a bunch of apps on the phone to save some battery power or to improve performance.
To close a single app, double-click the Home button. All of the open apps appear in smaller form. To close any of them (expect for the Home screen) slide (or flick) them up. This will close the app and free up some operating memory (not storage space) on the iPhone.