Scrub your skillet thoroughly with dish soap and a stiff brush. Generally you do not clean cast iron with soap because it removes the protective coating, but since you are going to season it, you want to start with a clean surface. Also, cast iron will often come from the factory with a waxy coating that must be removed prior to use because it is not safe to eat.
Melt the vegetable shortening and apply a thin layer on the bottom and sides of the skillet with a paper towel.
Bake the skillet in your oven at 350 degrees for about one hour.
Remove the skillet from the oven and let it cool off on your kitchen counter.
Repeat steps 1 through 4 if desired -- an additional layer will help maintain the coating for a longer period of time.