Children can be exposed to the game as early as they are able to swing the club.  In fact, children make the best students.  Adults are more analytical and try to incorporate logic and reason into a golf swing.  Adults can easily fall into becoming "mechanical" or even worse, "technical".  Children have no pre-conceived notions of what is right or wrong because it is truly a new experience.  If you ask a young person to swing a particular way, they will do it correctly from day one, where adults can tend to resist the change and repeat the same mistake.  It is for these reasons that a child's exposure to the game cannot begin too early.

In retrospect, the key ingredient to a young student is attention span.  Younger children are many times interested for much shorter periods of time.  One thing that can help is to make it as much fun as possible and try not to drag out the sessions for too long.  If you make it work for them right away, they will not enjoy it as much.