Use a utility knife to smooth the edges of the crack. If the crack is from old drywall tape, cut it at the ends where it is not cracked and then score it parallel to the tape. Use the tip of the knife to pry up the tape and pull it off. Sand the edges of the wound smooth and even. Any crack needs to be sanded to flatten it and to rough up the surface so the compound will stick.
Use a small brush to clean any dust or debris out of the crack. Finish with a lightly damp rag to really get the last of the dirt off the surface. Little particles will keep the finish from adhering and, in the case of drywall tape, will prevent it from sticking. Allow the area to air-dry completely before proceeding.
Repair the crack from faulty drywall tape by replacing it. Cut a piece of tape the length of the area. Put some drywall mud in the pan and add just enough water to thin it slightly. This will make it easy to skim over the area. Use a drywall knife to mix in the water.
Skim some thinned drywall mud over the old joint tape area. Fill in the depressions. Push the tape in place and run the side of your palm over the length of the tape to press it into the mud. Use a moist rag to wipe away the mud that presses out from the edges of the tape. Allow the area to dry enough for sanding. Drying times will vary, depending on the thickness of the layer of drywall mud and the temperature and humidity of the room where you are making the repairs.
Sand the edges of the repaired area so they are flush with the wall. Wipe off the dust. Mix a small thinned-out batch of drywall mud. Dip the drywall knife in and scoop up just a little of the mix. Skim across the area with the mud at a 45-degree angle. You are trying to leave as little as possible but cover any edge marks. Feather out the mud at the edges and corners. Scrape over it lightly and repeatedly to remove any thick spots. This may take some time. Allow the mud to dry and then paint over it.
Fill cracks that were not caused by seams or faulty drywall tape by skim-coating over them with the mud. You do not need to thin it, but scrape the product over the crack, pushing the mud into the crack. Allow it to dry and then feather out the top. Allow that to dry and then lightly sand off any imperfections.