Monsters are most commonly employed as mounts for characters. A monster and its rider or riders count as a single model in the same way as a cavalry model, although different rules apply.
Horses, wolves, warboars and other similar sized creatures that only have 1 Wound are covered by the rules already described for cavalry. As you will recall, a mounted Knight is a cavalry model. If the Knight is slain then the complete model is removed including the horse be is riding. To represent the value of the horse and to make cavalry appropriately resilient an extra +1 is added to the Knight's saving throw, but otherwise no account is made of separate casualties for mount and rider.
This system is fine for these smaller creatures, but obviously wouldn't work for big monsters such as Dragons which are far larger and much more difficult to kill than a horse or a wolf.
If a mount has 2 or more Wounds then it is classed as a monster and the following rules are used for riders and mounts. These rules would therefore apply to a Hero riding a Griffon, a Wizard mounted on a Wyvern, a Dragon and its lordly rider, and so on. No additional +1 is added to the rider's saving throw, as the advantages of riding the monster are worked out in other ways instead.