Cut out loose pieces of plaster around the crack using a utility knife. Ensure that you have solid plaster to which you can apply the joint compound to fill the crack. Use a 6-inch drywall knife to scrape off old paint that has bubbled or cracked. The goal is to clean the area of any and all loose material.
Dig enough joint compound out of the bucket using the 6-inch drywall knife to cover the bottom inch of the blade.
Spread the joint compound into the crack and onto the good plaster around it. Work the joint compound deep into the crack so the material fills the gap completely. Hold the drywall knife at a low angle to the wall's surface when spreading it and at a wider angle to scrape off the excess. Allow the joint compound to dry for 24 hours.
Sand the repaired area using a drywall sanding screen. Remove any bumps and ridges and make the surface as smooth as possible. Apply another coat of joint compound if there are still low areas that did not fill in completely with the application of the first coat. Allow the second coat to dry for 24 hours and sand it smooth.
Paint the repaired area with a paintbrush, applying paint that matches the rest of the wall. Feather the edges of the repaired area lightly with the brush to blend it into the older paint.