Remove chipping paint near the crack using a putty knife. Don't vigorously force old paint off the wall; only remove paint that is already loose. When a wall cracks, it almost always pulls some paint up, and existing loose paint will lead to new chips and blemishes later on if you don't remove it.
Apply plaster patching compound to the wall crack using a putty knife.
Smooth out the plaster patching compound with the putty knife. Wait for the compound to dry. Fast-drying plaster patching compounds take only an hour or two. Other compounds must set for an entire day. Consult the packaging to see how long your patching compound needs to set.
Sand the surface with 150-grit sandpaper. A freshly patched crack is usually rough and slightly uneven, even after smoothing with a putty knife. Sandpaper makes the surface level and ready for painting.
Wipe off any plaster dust using a moist rag. Don't saturate the wall. The rag should be just moist enough to clean without getting the surface very wet.
Paint the patched wall with latex paint and a roller or paintbrush. Fresh plaster covers very easily with new paint, often in just one or two coats. Wait for the first coat to dry before applying any additional coats.