Cut out any loose pieces of plaster from the damaged areas using a utility knife. Use the side of the knife's blade to scrape the loose parts free. The goal is to leave only solid plaster to which you can apply the joint compound.
Sand the damaged areas smooth with a drywall sanding sponge. The sanding prepares the surface to better accept the joint compound.
Fill a drywall pan halfway with joint compound so that it is not so heavy to hold. Hold a 6-inch drywall knife in your dominant hand with an over-hand grip and place your index finger on the back of the handle. Scrape some joint compound out of the pan with the knife so that it forms a 1-inch-wide bead of compound on the edge of the knife.
Feather the joint compound over the damaged areas with the knife. Hold the knife at a low angle to the surface to apply the joint compound and at more of an angle to remove excess compound. Apply the compound using an upward motion and remove excess with downward swipes. Work the joint compound onto the surface so that it is as smooth as possible. Let the joint compound dry for 24 hours.
Smooth the surface by sanding off any bumps or ridges using a drywall sanding sponge. Hold the sponge in your dominant hand and lightly move it over the surface in locations that are not entirely smooth or even.