Yizkor is not required to be said at all, but it is the custom in most places. Yizkor is normally said on Yom Kippur (and the final day of Passover, the second day of Shavuot and on Shmini Atzeret), when many people attend the synagogue prayer services.
Yizkor may be said anytime you wish—even when it is not a Jewish festival--and does not require a minyan.