This is the only shortbread recipe I've even been successful with, and it is the simplest.
You will need:
(makes about 32 wedges)
3 cups sifted all purpose flour
1/2 cup sugar
1 cup soft butter
1 egg yolk
Mix the first three ingredients together using your hands. Add the egg yolk and really work and knead the dough. Divide it in fourths and continue to work each until smooth (this takes some wrist strength). Form into 4 rounds and roll to 1/2 inch thickness. Cut into wedges and prick with a fork. Place on an ungreased cookie sheet in a pre-heated 300 degree oven. It will take at least 30 minutes, and likely more depending on your oven. The tops will not brown, but the bottoms and edges will. I'd check in three minute increments after thirty minutes. It may take as much as an additional fifteen minutes, but best to stand nearby in the event they suddenly begin to burn. They will be quite soft and should carefully be removed to a rack to cool.