Much good advice previously posted. Sunnies with a soft / slow glass rod to start; focus on roll cast; fish when they want to fish, goof around when they want to goof around. I've taught many kids, and these bits from previous guys really caught my eye.
Quick tip: Get a dowel about 2 feet long and have the kid fling a plastic bottle off the tip. If they can control flinging the bottle, they can control where the cast goes when they're using a rod.
Knots are important and kids do not have fully developed finger dexterity / fine motor skills until somewhere in the 6-7-8 range. It varies.
My dad started taking me at 4-5, but I was just pulling them in when we fly fished. Only on small creeks (mainly Rose River in Blue Ridge region of Virginia).
When the kid lets you know he or she is ready / old enough, action is still very important. If you're lucky enough to live near a creek with a hickory shad run, take full advantage. Hickory shad will swat a fly, and sometimes if you miss the first or second one on a single cast, you may get a third hit on the same cast.
Super important thing to remember: A kid who weighs 30 pounds is easily washed away, and it takes a lot less water than you might think to do it. A tiny trout stream will have a flow of 10 cubic feet per second. A cubic foot of water is just shy of 7.5 gallons. A gallon of water weights just about 8 pounds. When a 30 pound kid wanders into a fast-flowing spot (which they will do like a dog to something stinky) on that small 10 CFS creek, they're facing 600 pounds of water per second. It doesn't look dangerous, but it certainly can be, especially if the air temperature is under 60 degrees. They may not be swept away, but being cold and wet from an early season full fishing baptism is at best unpleasant.
To many of us, respect for water is so second nature, we sometimes forget about it, but when we're dealing with the little guys, we need to focus on the basics.
The most important thing of all: Take kids fishing, make sure they enjoy it, don't plan on fishing yourself, and be sure to point out the wonders of nature. Our time to enjoy fly fishing the streams of this earthly estate is limited to our time as mere mortals. We transcend this and fish on into the ages when we pass the skills and enjoyment on to the next generations. It makes me happy to think I'm fishing for my dad and the half dozen or so guys who taught him how to fish back in the 1940s when he was a boy.
I am hopeful my son and the other boys and girls I've taught to fish bring me along when they go fishing and I've moved on to the great beyond.