Here's what I did.
Before they are old enough to shoot, let them help you clean the guns after a trip to the range. This gives them a chance to handle the guns and you to teach them about pointing the muzzle in the right direction, keeping finger off the trigger, etc. Talk to them about the sight picture.
When they are old/magture enough to concentrate well enough to keep focused long enough to be safe, I started mine on a .22 rifle. Single shot was my preference. Allows them to focus on each shot. Sandbag he front if they aren't strong enough to hold it up without shaking. Sitting at a bench or prone worked best.
Progress to .22 handguns next. Lightweight is key. They have to be able to hold it steady.
Talk to them ahead of time about what will happen when they pull the trigger. Any recoil or loud noises should not be a surprise. Nothing should scare them.
Progress after some time to a larger rifle as they can handle it. I started mine out at 5 or 6 years old and stepped them up to a .22 hornet and a .410 shotgun after 7 years old.
Always have fun cleaning the guns together afterwards.