Choose an appropriate medium. There are actually many different mediums that can shade a drawing with a deep, inky black. The type of medium you choose should depend on your tastes. Pencils may be what spring to mind first. If you're going to use a pencil, try a pencil with a soft lead--either 4B or softer. Charcoal works well to create black shadows, as does pen and ink. Note that each medium has pros and cons. Pencil is easily controlled, but is more gray than black. Charcoal is very black, but also messy. Ink is a very dark black, and less messy, but can be difficult for creating a gradient effect.
Shade the shadow starting from the darkest part and outward toward the lighter parts of the shadow. Start by shading lightly at first. If you are using a medium like pen and ink, hash marks can be used to represent shadow. Light shading can be represented with hash marks by making the lines of the hash marks far apart, with a great deal of white space in between them.
Blend the edges of your shadow with the white parts of the page if you are working with a medium like pencil or charcoal. Use your finger to smudge the mark, or use a blending stick if one is available. To blend the edges of the shadow with ink hash marks, allow the hash marks to become lighter and lighter as you approach the edges of the shadow.
Deepen the shadows in the darkest parts as needed and work outward to the lighter parts, lightening the amount that you are shading as you go. Continue to blend at the edges. Repeat this step until you have shaded the page the desired amount.