I started my kids (1 girl and 2 boys) fly fishing very early at about age 3 by taking them to a small stream (not more than 20' across in the beaver ponds) close by that was fool of small brookies and cutthroats. I took a 7'6" 4 wt rod and some dry flies, made a cast, handed the rod to my young 'un, had them set the hook when the fly disappeared, and reel in the fish. All three of them loved it!
We also took them to a small pond that was full of panfish with the same rod and small poppers. They also loved catching bluegills and crappie.
At age 6, we got a medium action 7' 4 wt rod and I taught each of them to double spey from the right bank and snap-T from the right bank with it by using both hands. Using both hands took care of the problem of wrist strength and the double spey and snap-T eliminated the problem of having to learn how to make a backcast. We took them to small steams or ponds and let them cast to the fish themselves. Although both my wife I and took our rods along because the kids insisted we "fish" too, we never made very many casts and spent most of our time watching, coaching, and helping them remove tangles or tie on new flies. The three of them still talk about how cool it was and how much fun they had, and their ages are now 13, 18, and 25. In other words, don't expect to do much fishing if any yourself until they reach about age 8 or 9, at which point they will want a different rod.
As was mentioned, be prepared to let them rumage around in the water turning over rocks, etc. to find nymphs, larvae and assorted other things. They all let us know when they were tired of casting or fishing because they would just put the rod down and start looking for bugs. Be prepared to answer a ton of questions about the bugs and why fish eat them because eating a bug is gross.