As a single model, the monster and its rider are considered to be a single target. It is not possible to shoot specifically at either the rider or the mount unless the shooting model has the Sniper special rule.
Once you have established how many hits have been scored, you must apportion them between the rider and the monster. For each hit scored roll a D6: on a roll of 1-4 the monster has been hit. On a 5-6 the rider has been hit. If a monster has two or more riders (a very unusual combination) then on a result of 5 or 6, randomize any hits among the riders.
Roll to wound the monster and rider as normal, remembering to roll the dice separately so you can tell the two sets of hits apart. Once you know how many wounds have been inflicted on the monster and the rider, they can each take any saves to which they are entitled.
If you use a weapon or spell that uses a template against a monster mount, both the riders and the mount are automatically hit if the monster's base is touched by the template (note that this includes bouncing cannonballs!). In the case of a stone thrower, which inflicts hits at two different Strengths, only one model will be hit at the higher Strength (assuming that model'sbase is under the centre of the template). Randomise, as for a shooting attack, to see whether one of the riders or the mount is unlucky enough to take the high- Strength hit. All other models are hit at the lower Strength value.