I started with my oldest when he was 4 with a pellet rifle and a .22. I just took one of my 6 year old twins to shoot the 22 for his first time last weekend.
I did a little safety talk at the house when i pulled the .22 out of the safe and explained where the muzzle should always be pointed, treat a gun like it's loaded, finger off the trigger and then i setup a rest and let each one of them shoulder the rifle just to see how well they were listening. We also go over what to do if they ever find a gun.
Then in the truck right before we walk into the range, i explain that they need to stay within an arms reach of me and not touch the weapon unless told to. And as mentioned above by 2britts, make it fun and get excited when they make a good shot and don't focus on all the mechanics of shooting. It can be hard at times for them not to follow all of the directions and tips, but as long as they staying safe, let them have fun and the accuracy will get better with time and experience.
With 3 boys all at shooting age, i'm trying to make it a point to get individual time with them and take them to the range so they become more comfortable shooting and get some one on one time.
Good luck and have fun.