Clear away any loose drywall or debris from the crack.
Cut a piece of drywall tape to fit the length of the crack plus about 1/2 inch. Apply the tape to the area, overlapping it a little on either end.
Dip the tip of a putty knife into the joint compound and scoop out a small amount.
Smooth a thin layer of joint compound along the crack, using the tip of the putty knife to skim off the excess. Make sure the tape is completely covered with the thin layer of joint compound.
Allow the joint compound to dry for several hours. The joint compound may shrink into the space leaving a concave appearance once it dries. If this happens, apply another layer of joint compound, smooth it with the putty knife, and allow it to dry. Don't worry too much about overfilling the space a little, since it will be sanded down once it dries.
Lightly sand the area with medium grit sandpaper until smooth. Brush away the sanded particles, prime and paint with touchup paint.
Cut an angled tip off the tube of caulk. Squeezing the tube with steady pressure, place a small amount of acrylic caulk along the crack.
Wet the tip of your finger and smooth the caulk along the crack, pressing the caulk into the void as you go. Wipe off the excess with a damp paper towel.
Allow the caulk to dry overnight. If the caulk has shrunk into the crack, apply another thin layer to make it level with the surrounding area. Allow it to dry, then prime and paint the repair with touchup paint.