Cut a piece of cardboard into an 8" square. This square will be the base for the top of your graduation cap.
Cut a piece of fabric in your desired color and material into a piece that is 8 ½" wide and 17" long. Lay fabric pattern side up. Fold your fabric over itself widthwise, pattern side in.
From the fold out, sew along the opposite of your fabric, approximately ¼" in on each side. Leave the side opposite from the fold un-sewn. Cut off any excess material and turn inside out.
Insert your piece of cardboard into your fabric. Sew the open side closed by hand, cutting off all excess material.
Use a large needle to poke a hole through the top center of your graduation cap. Thread your needle and attach your button through the hole. This will be the holder for the tassel of your graduation cap.
Cut your sheet of poster board into strip that is approximately 3 ½" wide and 24" inches long. Wrap around the head of the intended wearer to be sure the length is correct.
Cut your fabric into a piece that is 4" wide and 25" long. Fold in half lengthwise, pattern side in. Sew along the long edge (approximately ½" in) of your poster board and one opposing end. Cut off any excess.
Turn inside out and insert your poster board strip. Sew last edge closed by hand. Cut off any excess for a snug fit.
Bend your strip into a circle and connect the ends with straight pins. You can sew these ends in place by hand, or with your sewing machine.
Position your circle on the underside of the lid of your hat. Attach to the lid of your hat with hot glue, or sew in place by hand.