It all depends on the child, AND YOU. First, a person has to determine if he or she has the patience to teach a child the importance of gun safety and shooting. Only after a person is ready, will he or she be able to determine whether the child is ready.
A child can be ready at pretty much any age. There should be no arbitrary cut-off date of 8, 9, or 10 years. All children exhibit different levels of maturity and responsibility at a given age.
Also, the degree of initial exposure to guns should also be determined. A child may not be able to shoot a centerfire rifle until, say, 10 years old, but could be involved in watching his father shoot (safely) while the child is still in his or her diapers. Similarly, a child can be, say 5 years old, and, with his father or mother by his immediate side, shoot one of those toy guns that shoot out those popping corks.
Conversely, I believe that there is such a thing as waiting too long to teach children about guns. My father didn't take me hunting until I was about 9 years old, but I remember having a fascination with guns well before then. As a result, I would go into his closet, get the gun case, open it up, and hold the gun (my father always had the shotgun unloaded). Yes, you can say that my father should have kept it in a safe or a vault with trigger locks etc. Well, we were very poor then and things like trigger locks didn't exist. Still, the best safety was for him to not only teach me about guns, but more importantly respect them - which he did, but in my later years of about 9 or so.
You can start teaching your children about guns at a VERY early age. You can teach them how to SHOOT guns at any age that they are physically, and mentally, ready.
Again, don't have arbitrary dates because each child is different.
Zachary