Measure the circumference of the head of the person who will be wearing the hat with a measuring tape. Note that measurement. Measure down from the top of the head to the location on the forehead where you would like the hat to hit. Write down that number.
Draw a half circle on a sheet of paper that is half the circumference of the head plus 1 inch, so the hat is not too tight. This will be the template for your hat.
Cut out the hat template, and lay it on the piece of black felt. Cut around the template so you have a black-felt half circle. Repeat the process so you have 2 felt half circles.
Place the felt half circles on top of each other and, using your needle or sewing machine, sew a 1/2-inch seam along the curve from 1 corner toward the center. After sewing 4 inches, stop and leave an opening that is 3/4 inches wide to accommodate an ear.
Move your needle to the other corner and begin sewing once more, making a 1/2-inch seam toward the center of the curve. Sew 4 inches along the curve, then leave a 3/4-inch opening for second ear. Finish sewing the hat by sewing the area between the 2 openings closed.
Turn the hat right-side out, so the sewn edges are inside. The hat portion is now complete.
Draw a 2-inch-wide circle with a flat bottom that tapers in on a piece of paper, and cut it out. This will be the template for your ears.
Cut out 4 black-felt circles using the ear template. Cut out 2 circles from the cardboard, also using the ear template.
Lay 2 of the black circles on a flat surface, and attach the cardboard circles to them using a hot glue gun. Attach the other black felt circles to the other side of the cardboard with the hot glue gun. Allow the glue to dry.
Insert the ears into the openings you left on the hat. Push the ears down 1/2 inch.
Turn the hat inside out, holding the ears carefully in place. Using your sewing machine or a needle and thread, sew the ears into place. Turn the hat right side out.