Coarser grit sandpaper should be used in the first phase to bring down the rough areas. Avoid the temptation to use very coarse grit sandpaper; this will abrade the drywall paper surface.
Follow up with a lighter grit sandpaper in the second sanding.
Small areas of joint compound can be "sanded" with a wet sponge, called the "wet-sanding technique." This is a great way to help reduce drywall dust. Another way to reduce dust is to use a barrier system such as ZipWall.
