The way I started out was snake hunting with a .22, but being on the road so much, my kids don't really have the same opportunities that I had.
My way of getting my kids comfortable was just shooting stuff around the house...perks of living way out. My oldest kid started out shooting pine cones, gum balls, and stumps. Then he made his way into squirrel hunting with a .410 behind my dog. Now he probably didn't touch a strand of fur, but if you asked him, he head shot every one of them.
Biggest thing to me was trying to make it fun and challenging. Every kid is different though. My youngest boy is a little more competitive, so presenting a challenge was more important with him. I would shoot at something and then tell him "bet you can't do that". He will shoot till the cows come home. But if you just set him down and say "let's practice", he will lose interest after about two trigger pulls.