I needed two batteries because just one wasn't strong enough.
One 9V battery should be plenty to power the Arduino. Whether it is enough to power all the stuff attached to the Arduino, too, depends on what that stuff is.
Keep in mind that 9V rectangular batteries belong in smoke detectors, not Arduino. The current per $ ratings are way too low to be cost effective.
4 AA batteries in a holder are about the same size as an Arduino, and will last a lot longer.