This works well on a flat sheet of paper, but the real world is 3-dimensional and sometimes it is necessary to label points in 3-dimensional space. The cartesian ($$x,y$$) labeling can be extended to 3 dimensions by adding a third coordinate $$z$$. If ($$x,y$$) is a point on the sheet, then the point ($$x,y,z$$) in space is reached by moving to ($$x,y$$) and then rising a distance $$z$$ above the paper (points below it have negative $$z$$).
Very simple and clear, once a decision is made on which side of the sheet $$z$$ is positive. By common agreement the positive branches of the ($$x,y,z$$) axes, in that order, follow the thumb and the first two fingers of the right hand when extended in a way that they make the largest angles with each other.