Great question. I had my son (Johnny aka .308 Master) out in the field at 5 years of age (tagging along) and he carried a Daisy Red Ryder (unloaded). We did this so he could be corrected in the field while "tagging along". At the age of 6 years, for X-mas Santa bought him a Marlin youth .22 (Little Buckaroo) and he scoped it with a Leupold Vari-X III fixed power 4X. Santa also got him a spinning .22 target (which we still have).
At this point he understood the manners of general safety and my buddies and I would have .22 shooting contests with the spinner which he participated in and was enthusiastic about. The lessons continued. I won a 20 gauge Remington Wingmaster Magnum at an SCI banquet and at age seven we converted it into a youth gun by buying a youth stock (which Fred aka Snake Charmer cut down further) and a short barrel along with a Past recoil shoulder harness. We spent countless hours at project 2000 on the 5 stand. He did very well so his hunting career started thereafter. From there he was shooting dove, honkers etc. with that little 20 gauge.
In the meantime he continued to shoot his .22 any chance he could. And for his 12th birthday we went down to Fine Firearms
http://gunssandiego.com/ and we purchased him a Remington 700 Youth rifle with plastic stocks in .308 Winchester - topped it off with Warne scope mounts and a Leupold Vari-XIII in 2.5 - 7. Also for his birthday we took him on a real pig hunt in Paso Robles. He slayed his pig (150 yard shot - Barnes X) and that same year he also shot his first elk in New Mexico.
The bottom line is - a kid is not ready until he/she is ready. It is all about the time invested as well as what was retained. My son has been the safest person I have ever hunted with since he stepped into the field (Snake Charmer & Justmygame can attest to that). And I believe it is because of the investment made by me and my hunting partners.
The investment paid off for us, me and my buddies drug that little guy all over the South Western united states, through snow/heat/long road trips etc.- something I will never regret.