That pretty much means that oxygen can either gain 1 electron (-1) or gain two electrons (-2). It is just that oxygen anions with a oxidation of -2 is more common.
Much of the main group elements do not have many common oxidation states. It is only when you get to transition metals and some lower period main group elements where you have multiple oxidation states. And yeah, I suppose memorizing the common ones for some (not all, that would really bite) is a good idea.