Shape the sock by flattening out and smoothing the part of the sock that will be used for the mouth.
If you have a crew style sock, this will be the preformed heel part that you push in.
Cut a piece of material in the shape of a circle that is the width of your sock. When folded in half, this will form the inside of the mouth.
Attach a small piece of contrasting material to be the tongue. Sew that in place. It can also just be glued in to the bottom half of the mouth if you do not want it to flap around.
Cut a slit in the sock a little less than the width of the sock at the halfway point where the mouth would fold up. This is an access hole for your fingers to move the mouth. When the mouthpiece is sewn on to the sock, it will form two little pockets for your fingers to grip.
Crease around the edge of the piece that you will use for the mouth to create a stronger hem. Sew this to the sock. It is a good idea to mark the circle of the mouth so you know where to sew when all the fabric is moving around. You could pin it in place but that was too much trouble.