When my daughter was five, I bought her Marlin 15YN single shot, bolt action youth rifle in .22 lr. I put a brass oval plaque on the right side of the buttstock that read, "To My Daughter Lauren 2002 Love Dad."
I wanted her to shoot it at my parents' log cabin in Wisconsin. I have photos and video of her shooting her Marlin. She sat in a chair at a table and worked the bolt, inserted a round, and kept her finger off the trigger. I drew a sight picture for her on a piece of paper. We were shooting at piece of steel hung in front of our backstop 75' away.
She hit it on her first try. I taught her to keep her finger off the trigger right from the start. At first, she liked the way the bolt threw the empties out more than the actually shooting! But she really liked hitting that steel gong.
As the years went on, she grew into the Marlin. At 12, she can place extra rounds between her left hand's fingers as she holds the forearm and load each shot quickly from a standing position. She never misses either.
I bought her a Colt Bat Masterson 1967 commemorative (unfired in a presentation case) as her first handgun.
She fired her first Cowboy Action Shooting match earlier this year. She fired six stages totalling 145 rounds (in her Colt and in my Ruger Single Six, in my Marlin 39M, and in my 12 gauge Rossi side by side, exposed hammer shotgun) and only missed one shot. She had one round that didn't go off but she worked right through it.
She enjoys shooting with her whole family because both my wife and I and my wife's dad (Lauren's grandpa) all shoot together. Three generations. There are few things in life as rewarding as sharing something you love doing with your family.
Here she is shooting her Colt:
Here she is shooting a CAS stage (video):
I asked her if she'd like to try shooting trap with her great-grandfather's Browning Twelvette. She hit 15 out of 25 her first time!
When I went to try out my .22 conversion kit for my Sig P220, she really enjoyed loading the magazine, racking the slide, and then shooting the semi-auto at the targets.
We shoot a pellet rifle in the backyard and we print out fun targets off the internet to shoot at.
I think the best thing is to not push shooting too hard. Let a child learn at their own pace. Try to make things interesting with unique targets or reactionary things. Remember that shooting a black bullseye isn't very rewarding. Kids crave stimulus and Necco wafers glued to a target's bullseye explode in a puff of smoke when hit, even with a .177 pellet.
Don't try to force a kid to shoot too long. Don't stress accuracy too much, just repeat sight alignment, breath control, and trigger squeeze.
When I could tell my daughter was getting bored or tired, it was time to stop for the day.
I guess the best advice is to make shooting fun and not a chore.
It's worked for me and my daughter enjoying range time with her dad is amazingly rewarding for both of us. I'm very happy to be carrying on the tradition that my dad, my grandpa, and my great-grandpa kept going all those years....
-Steve