I grew up around firearms.
My grandpa was a justice of the peace then a deputy sheriff (35 odd years, iirc). He always had multiple firearms in the house (one handgun on his nightstand, one on my grandmother's; rifle rack with two shotguns and two rifles over the sideboard; 22 bolt action propped behind the back door along with his walking stick.)
When I was small (< 5 years) I knew what guns were, but wasn't allowed to do more than look. When I was 5, my grandpa 'helped' me shoot a 410 shotgun, a 32 revolver, and that bolt action 22- contrary to my mother's wishes (what are grandpas good for, if not to spoil their grandkids.) When I was 7 or 8, I got a pellet gun for christmas. My dad taught me gun safety, the four rules, how to clean and care for a couple of different guns. I had to be able to name every part, explain how all the different parts worked (not down to the technical detail, but generally.)
From 8-10 I shot under supervision, mostly with my grandpa. Most of the time we'd just shoot tin cans or pie plates, but there were a few infamous exceptions- Here's a pic of the foxes that me and my grandpa shot when I was nine- the cut under my left eye is from me crowding the scope. My mother was furious that he a) let me shoot unassisted and b) with such a big gun (Winchester 30-30 iirc). We shot at the exact same time. :)
(sorry for the picture quality, it was a polaroid instant in the 70's)
When I was 11 or 12, an uncle gave me a bolt action savage 22. I had been shooting the bb gun unsupervised, but for the 22, I had to have permission / supervision again. By the time I was 14, I was taking day trips into the woods behind our house during squirrel & rabbit season unsupervised with the 22. (My grandpa had been teaching me woodsmanship since I was big enough to not be carried.) By 16, I was spending weekends in the woods- ostensibly to hunt, but often just to enjoy the scenery or to dig ginseng for spending money.
Almost every November from the time I was old enough to remember until I was 16 or 17, me, my dad, his brothers, and some cousins took off two weeks and camped in GW national forest (Bath County, VA) to go deer & turkey hunting for meat. It was serious business for us back then, as we were dirt poor, and that meat lasted well into July some years (mixed in with cheaper meats or separate.)
If I had kids, I think I'd start with 'eddie eagle'-like material at an early age- don't touch, call an adult, etc. All guns would be locked up in a child proof cabinet.
Around 7 or 8, I'd explain that guns are dangerous, and can kill. Break any potential fascination but don't instill irrational fear, either. Treat guns like an open flame, or a sharp knife- a useful but dangerous tool. If I had an area that I could shoot a low caliber gun like a 22, I'd do so with something like an apple or a melon, just to show that they deserve respect.
Then at 8-9 teach them the rules, and introduce a bb gun or airsoft. Have them treat it as though it were a real firearm. This would be where they get to prove that they are responsible (and you get to evaluate just how ready they are to go to the next step.) Make sure that any violation of the rules of safety will have consequences- my dad threatened to keep my bb gun for six months if I had ever broken a rule the first time, and he'd destroy the bb gun if there were a second time.
Around 10, I'd start with a youth model 22 if I had a place to shoot it close by. I wouldn't suggest a range, as that's noisy and potentially scary to a kid whose exposure to guns up until then had been a bb / airsoft gun.
A friend of mine has a pink 'cricket' 22 (
http://www.crickett.com/CrickettRifle/crickettrifle.html) for his 9 year old daughter, they go shooting every couple of months.
When he first started teaching her to shoot, he'd hold the gun and let her sight it and pull the trigger. Once she had the strength to hold the rifle steady (the cricket is only 2.5lbs), he started removing the hand holding the front of the rifle. He's teaching her a little early with a 22 for my taste, but she seems to be responsible, always checks to the sides and in front of her when she's preparing to shoot, always looks around before shooting to make sure everyone has their 'ears on'.