Using sandpaper that is too coarse -- in the hopes that you can speed up the sanding portion of drywall installation -- will only end up marking up the drywall. For the second and, especially, the third layers of drywall mud, use either a 120-grit or a 150-grit sandpaper. Use a 220-grit sandpaper for the third layer if you want to give the drywall an even smoother finish. Use a medium-grit sandpaper for the first layer of mud, such as a 100-grit sandpaper.
To sand the drywall, you can simply fold a sheet of sandpaper and hold it in your hand while sanding. Another method is to wrap the sandpaper, abrasive side facing out, around a block of wood. Stand on a ladder to reach high wall areas. For general wall areas, install sandpaper on a hand sander, which is a hand tool that has a handle you grip and a flat surface for the sandpaper, which is often held in place by clips. Sand both low and high wall areas and ceilings with sandpaper installed onto the end of a pole sander.
Sand drywall lightly to keep from gouging the drywall surface. Sand it using just enough pressure to remove the ridges and bumps on the drywall. The mud is fairly soft, and if you sand too hard, you end up going through the compound and exposing the drywall tape underneath it. Also, wear a dust mask while sanding, because dust particles will constantly enter the air as you work. Wear goggles to keep the dust out of your eyes, and also wear a cap to protect your hair.
Because sanding is such a dusty job, some drywall installers use a drywall sponge on the third and final layer of drywall compound, especially if the compound is fairly smooth already. Using a sponge takes a little longer than using sandpaper, but you do avoid scraping dust into the air while you work. The sponge softens and smooths the drywall. If you use a sponge, keep a bucket of warm water beside you, and dip the sponge into the water, squeezing out any excess. Use circular motions with the sponge on the drywall, and constantly rinse the sponge in the bucket while you work, always using a wet sponge. Use a medium-grit sponge on the first coat and a fine-grit sponge on the second and third coats.