I taught my 6 year old to knit a few weeks ago.
I just used whatever I had on hand. She wanted to learn because she saw me do it. Frankly, I was very skeptical. My daughter is a big whiner, a quitter, and doesn't always have patience.
I gave her size 7 aluminum needles (because they were the only straights available) and some acrylic yarn. I knit continental, but I taught her to knit English. To my surprise, she caught on right away.
We used the little nursery rhyme method. I believe it went something like, "through the door, around the stack, through the front window, off jumps Jack."
I didn't teach her to purl so we're just doing everything garter stitch right now
But she's happy and was capable, even though I didn't at all think she could do it.