You start with a small square of green felt - about 4"x4" and a strip of red about 1"x4". Stitch the two pieces together.

Open the felt up so that you have 1 long piece and then fold it in 1/2.

Next, you need to stitch out the elf hat shape. It is much easier to stitch the shape out onto a rectangle than to cut out the shape and try to get everything lined up. Felt does stretch.

Next, you need to trim away the excess felt. BTW I would actually use green thread in the real project, but for the tutorial I used white for you to see. Also, you need to cut the zigzag edge on the red.

Fold the red up.

Next, you should glue around the bottom edge of the hat and place it down on another piece of green or red felt. Then, trim away the excess. This creates the bottom of the hat.

I glued a pompom on the tip of the hat. Jingle bells are also cute.
Finally, you can glue the hat onto an alligator clip, small comb, or even a headband.