Old is signed like you are pulling on a long beard, as if your were an old man. You start the sign with your dominant hand formed into a fist at your chin, then you move your fist downward toward your chest. As you pull on the imaginary beard, 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 young and new are most clearly explained to your baby by contrasting two opposite objects, such as an old ball and a new ball, or a young child versus an old adult. It usually takes exposure to old and new or young 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.