I started my son on BB guns after a bad day at scout camp. At 7 years old we were at a scout camp and they a BB gun range set up. Up til that point, I had never had him shoot anything. No surprise, then, when he barely hit the paper. He didn't know how to hold a gun, didn't know how to aim, and came away on the brink of tears. I felt like a failure as a father and vowed to correct my negligence.
We set up a range in the basement, shooting from about 20 feet. Instead of boring paper targets, we shot at clay pigeons. I set up a big box with 3 flaps taped up, the open side facing us. I pressed nails into the back flap and hung the clays. That worked great. All the debris just dropped straight down in to the box, making cleanup a breeze.
I taught him how to shoot, with great emphasis on safety. His older sister eventually joined us. My son became so safety conscious that I made him the Range Officer and let him call range hot & cold when we shot together.
The next year at scout camp, he went into the BB gun part with much great confidence. That year they had them in the prone position. The instructor didn't do much more than point out the safety aspects of shooting and pointed the boys downrange. I spent the time to get my son in proper prone position and by the time he started shooting his 6 BBs, the rest of the scouts on the line were done and impatiently waiting for us to finish.
My smile and my pride were huge as we pulled the target and 5 of 6 were in the black and the 6th nearly so!
The instructor said, "Obviously he's done this before".
He's almost 10 and we still shoot BB gun in the basement and I take him to the range every so often (but not enough) to shoot an old Ithaca .22 lever action that used to be his great grandpas. I haven't had him shooting a pistol yet but soon I'll have him shooting my Ruger Mark I.
The age to start kids off shooting really depends on the kid. My son was fine at 7, but my daughter was 9 before I felt comfortable letting her shoot.