Draw a heavy line with your pencil on a spare sheet of paper. Take your finger and drag it from the line in one direction. Do this all the way down the line to see how far the lead will spread and the gradation of the color. This type of shadow is best for an object with a hard edge casting a shadow on whatever is behind the object.
Repeat the procedure using a paper towel covering the end of your finger. If you want your drawing to last a lifetime, it is best not to subject it to the oils on your fingers, though it is easier to smudge this way and it may be best to learn using a bare finger.
Draw a few light hatch marks on another section of scrap paper. These should not be applied heavily to avoid indents in the paper.
Smudge your finger or paper towel over the area in a swift, left-to-right motion. You can also add a circular motion if you would like the shadow to be rounder. Afterward, you should not be able to see any pencil marks, just a uniform smudge. This technique is best for soft shadows on a figure's face or other shadowed areas that do not have a hard edge.
Keep your hand from smudging other sections of your drawing by placing a clean piece of white paper under your hand while drawing.
Purchase a putty rubber eraser and Blu-Tack. Putty rubber will lift off light graphite marks from your paper, and can also be used for gentle smudging. Blu-Tack will lift off darker mistakes. If you are new to smudging, it is easy to get carried away -- these erasers will help you to correct over-smudging and clean up the edges of your shadows.