How do I patch a small hole in drywall myself?

For a small hole under about 4 inches, the easiest method is to use a self-adhesive mesh patch kit from any hardware store. Clean the area around the hole, stick the mesh patch over it, then apply joint compound (also called mud) over the patch with a putty knife, feathering the edges outward. Let it dry completely, usually 24 hours, then sand it smooth. Apply a second thin coat if needed to fill any low spots, let dry, and sand again. Prime the area before painting, otherwise the patched spot will absorb paint differently and look dull. For tiny nail holes, you can skip the mesh and just fill directly with spackling compound, let dry, sand, and paint.