Here's an easy way to remove the skin of an orange prior to using the orange in sections for a recipe. Bring about 6 cups of water to boil in a small pan. Ever so slowly, with an orange in a large soup ladle, lower it into the pan.
After about 20 seconds remove the orange with the ladle and when it is cool enough to handle start peeling the skin. You will be amazed at how easy it comes off.