The old sign looks like you are pulling on a long beard, as if your were an old, wizened man. You start the sign with your dominant hand at your chin in a fist shape, then move your hand downward toward your chest. As you pull the imaginary beard down, you may wiggle or add a curve to your 'O' hand going down, to suggest the wave in the long beard of an old man.
Signs like new are most clearly explained to your baby by contrasting two opposite objects, such as an old ball and a new ball. It usually takes exposure to old and new in a few different contexts for children to start to generalize the meaning of the word.
We usually teach the old sign in conjunction with the sign for new. You can talk about some old object (such as a toy, cup, or clothes) and contrast it to the new version.