Trim off all fat and discoloration, etc. with kitchen shears or a sharp knife from the chicken. Wash under cold water. Put a cup of full of all-purpose, flour into a plastic bag. While the pieces are still very wet, place them one at a time into the flour. Shake the bag to coat each piece. Melt about 1/3 to 1/2 cup of shortening in a pan on medium heat. Shake the bag again to keep the pieces from sticking together.
When the shortening is melted and very hot, remove the chicken from the bag. Gently shake off the excess flour and lay into the hot fat. When all the pieces are in the pan, cover with a lid and allow to fry about 5 to 7 minutes. Remove cover and check each piece to see how brown it is. When it is lightly golden brown, turn to fry the other side. Add salt and fresh ground pepper to each piece on the browned side. Cover again and allow the other side to brown. Season the second side. At this point, you may remove the cover and continue to fry the chicken to the desired "browness" you prefer. Turn often.
It should be nicely browned with a very crisp outside and a moist, tender inside. You may want to reduce the heat a little after you have browned the second side. Boneless, skinless chicken gets done much faster than meat with the bone in. Place than fried pieces on a wire rack covered with a paper towel to drain off the excess grease.