I got my son interested by taking him with me when he was a toddler.
He has been around guns now for probably 10 years or more now(be 17 next month) and I let him see what I was doing and handle some guns plus I let him help me with some reloading.
I took him out with me a few times whistling foxes probably a bit to early in hindsight as he was fidgety and couldn't sit still so I abandoned that idea for a while longer.
It starts out as curiosity and kids being kids want to touch and play with things and because dad or mum is doing something interesting kids want to see what the fuss is all about as well.
As he got older and became more interested in guns and hunting I was showing him how a gun works and all the time pushing the safety thing with him especially where the barrel was pointing in relation to people and to keep the barrel pointed down at all times and treat every gun as loaded until the bolt was out and put away although semi auto,pump and lever actions are always treated as loaded till cleared and put away.
Also identification of what he was shooting at is another big consideration as shooting a person or $100,000 stud bull or stud ram is not a great way to keep your guns or house.
The next thing was in a hunting situation especially on pigs was watching where people were in relation to where the mob was running especially as he has a 30/30 lever action now with a 10 shot mag so lead in the air is now more dangerous to where people are and also what's in the background behind the pigs or whatever else he's shooting at.
Start your kids out with a .22 and a couple of bricks of .22 ammo and a few of those spinner targets and let them loose under supervision and teach them safety, breathing and trigger control and make them clear the gun with each other every time so that it becomes 2nd nature and it makes them feel good that they're doing what dad and mum does safely.