I’m starting the project with a little black and white fellow: Mr. Penguin.
I used a technique quite new to me: Intarsia in the round. Intarsia is usually knitted flat, so there is no problem with yarn being at the wrong side of the colour patch. When knitted in the round you only go in one direction, so after one round your yarn is on the left side of your colour patch and your needle on the right side. In fact to knit intarsia in the round you actually knit it back and forth like knitting flat and connect your knitting to simulate knitting in the round.
It required several tries until I figured out the way the joins of the rows work best for me. I made a small tutorial on knitting intarsia with wrapped stitches here.
Check out the project page with a list of all handpuppets and techniques.