Protecting the flooring underneath the wall by laying down plastic dropcloths. You can tape these into place to keep them from shifting while you work.
Use a chisel to knock away any debris around the crack or hole. The edges need to be free of any hanging debris, no matter how small, to avoid having the debris get into the mud.
Apply joint compound over the hole with a drywall or putty knife. Use a sweeping motion and work upward. Use enough to fill in any holes or cracks, but do not over-apply. Scrape off the excess compound as you work. Let the compound set until it is hard.
Sand down the compound with a fine-grit sanding block. The surface should be smooth to the touch and flush with the rest of the wall. Run your hand over the compound as you work to help you find any uneven areas that may be hard to see.