Cut two pieces of foil into 4-by-4 inch squares for large eyes. For medium eyes, cut the foil into 2-by-2 inch squares, and for smaller eyes, cut the foil into 1-by-1 inch squares.
Roll the two pieces of foil into two separate balls. The foil will add support for your eye balls and also make them lighter so you do not add too much weight to your puppet's face.
Knead two 1-by-5 inch strips of Polymer clay until the clay is soft and pliable. You can knead the clay in your hands as the heat from your hands will help to soften it.
Cut two 4-by-4 inch squares of clay that are a quarter of an inch thick from the clay you kneaded. If you have medium-sized foil balls, cut two 2-by-2 inch squares measuring 1/4-inch thick, and for smaller eyes cut two 1 1/2-by-1 1/2 inch squares measuring 1/4-inch thick.
Wrap the clay around the foil balls, making sure to cover the foil entirely. If you need to, add a little more clay until none of the foil is showing. Smooth the clay to eliminate cracks and air bubbles.
Place a sheet of foil over your clay and the craft oven's grate in order to create a smooth surface. You do not want to put your clay balls on the grate because doing so will create lines and dents. You want to make sure the clay balls do not bake unevenly. Place the clay balls on the foil and set your oven onto the polymer clay setting and let bake for 10 minutes. Allow the clay balls to cool entirely before removing from the oven.
Paint the clay balls with white acrylic paint and allow the paint to dry. Add additional coats of paint if needed. Once dry, choose a color you want for the irises and paint a circle in the center of the eye measuring a quarter of the dimension of the eye size you created. Allow to dry. When dry, add a black spot in the center for the pupil.
Make your irises look more realistic using a toothpick. Use acrylic paints that are a shade lighter and darker than the iris color and alternate creating lines stemming from the outside of the pupil to the outer edge of the iris. Doing this will help create flecks of color in the eye.
Coat the entire eye with a high-gloss varnish. Allow to dry. Add a second coat. The varnish will make the eyeballs appear wet and shiny, creating a realistic look.
Place the eyes inside your puppet's eye sockets. Place glue around the eye socket inside the puppet's head and gently place the eyeballs straight inside. Allow the glue or putty to dry for 48 hours before using your puppet.