I was about 12 when my dad and grandpa taught me to shoot with a .22. I've been shooting ever since, so thirty more years of it so far.
I bought my sons a BB gun when the youngest was about 5 and the oldest 9. They plinked with it under supervision, and I taught them gun safety. My older son lost interest, but my younger son has been right there with me shooting ever since. I bought him his first real gun, a combo .22, 20ga shotgun, and .243 rifle with interchangeable barrels, when he was nine. He does shooting sports with 4H.
When he was also 9, I met my now-husband, who's a big trapshooter. He got my son started with a little trapshooting with a better 20ga at 4H and then got us both into the league shooting. My son will be 14 this year and I've backed off of league shooting so the ammo money can go to him. The kid is a natural, and my husband says he's much better than he was at that age. He'll most likely be squad leader of his junior team this year, we'll find out on Saturday.
He's gone hunting with me since he was eight too, so he understands what the gun can do. He shot his first birds with my father-in-law two years ago, and took his first big game animal, a bear, last year. I'm happy to send him out back to kill the rats in the woodpile with my pellet gun; I know my dogs and chickens are safe around him. I gave him a .30-06 rifle the day he went deer hunting for the first time. If he shoots 50 clay pigeons in a row, he's going to earn himself a 12 gauge too. Right now he's shooting mine. He's better than I am with it.
My husband also has raised his girls, who are slightly younger, around guns all of their lives. Any kid can ask to see any gun from the safe at any time. A parent or grandparent has to be present and we take that time to drill them in safety. It's to take the mystery out of them.
We also don't do toy guns in our house, as children can get confused going back and forth. My mom took my son to see his cousins, and was very amused by his safe handling of the nerf guns. It's ingrained in him that much by now.