Ever since I was a kid I have always loved making stuff out of clay. For me there is something really visceral and cathartic about physically pushing and pulling the medium to represent a specific character or thing. There's something gratifying as well about taking a flat, 2D image and building something dimensional to represent it. In any case you can relieve some stress building your own Club Penguin playmate and have fun doing it!
If you decide to bake your final result, verify on your packaging whether or not your choice of clay may be put in the oven, and if so follow the directions as all brands vary.
Start with a small rectangular block of clay for the body approximately 2" x 4" x 1" as shown. (Some polymer clays stain so be sure to tape down some wax or butcher paper to work on.)
Next use a plastic knife or other tool to cut the block so the bottom remains the same size as before but the top tapers at an angle as shown.
Soften the corners with your hands to make the body a little rounder and add two small, almost flat rectangular shapes for feet as show. Stand the body up and gently squish it down on the feet. This might be an opportune time to add a little more clay to the penguin belly (at your discretion) for an even rounder shape.
Add a small rounded oval for the beak and use a tool like a plastic knife or toothpick to carve a mouth expression of your choice. Add a small flat white oval for the white of the eyes and dimple the top in the middle as shown to separate the eyes. Add tiny black ovals for the pupils. Use two almost flat, triangular pieces that taper as shown for the arms (You can work with the extra clay that you cut off when you shaped the body since it's already tapered).
Add a white, flat, bib-like belly (see Step 4 image for the basic shape to cut). For extra credit create a tiny Puffle by making a small ball of clay, white for the whites of the eyes, black for the pupils, and a few little cones for the hair, and carve the mouth expression as shown. Don't forget to add accessories (hats, beards, etc.) to bring out your penguin's personality!