When my boys were little, I'm talking 3 to 4 years old, we'd set in the floor and clean guns after I'd been shooting.
We went over the safety rules. I'd tell them which gun was which, what the caliber was, where the safety was, etc. Every time we'd clean the guns we'd go over all that and I'd explain why cleaning/lubing was important.
If the boys had a question about one of the guns we'd get it out of the case/closet and go over the safety rules and then they could hold the gun and we'd ask questions and get answers.
The oldest one suddenly lost interest in guns/shooting about the time the youngest one got old enough to start shooting. Now that I realize he had severe anxiety issues about being compared to the younger one at least I know what happened (he also quit fishing with me and just about quit everything we did together). The oldest suddenly regained an interest in guns/shooting over a year ago and he's actually taken days off from work to go shooting with me. He's bought a CZ 75 Compact, too. He's showing an interest in some of my dad's guns and my father-in-laws guns (all 30 to 70 years old or more and just regular hunting shotguns and rifles, but hey, it's still an interest in guns).
The youngest has the disease almost as bad as I do. He's most always talking guns when we're together and goes to all the local gun shows with me. He goes shooting with me several times a year and recently decided he wanted to start reloading on his own (his house). He's reloaded his rifle and pistol ammo for several years now using my reloading equipment.
You've got to start early and make it interesting and enjoyable. If they have fun, they'll want to do it.