Sand down the cracked wall using a sanding buffer with a medium-grain sanding ring. This smooths down edges, chipping and roughness on the wall and around the cracks.
Vacuum the wall, surrounding areas and in the cracks using a shop vacuum.
Fill a spray bottle with water.
Cut a piece of plaster gauze patch to measure the width and length of one of the cracks, then place the patch over the crack.
Spray the patch with water to dampen it. This will moisten the plaster and allows the patch to adhere to the wall. Allow the patch to dry for 2 hours. Repeat to cover all of the cracks with patches.
Spread spackle over the patches using a flat-ended trowel. Scrape the trowel across the edges of the patches to make the edges flush with the rest of the wall. Allow the spackle to dry for 6 hours.
Sand the wall patches using fine-grain sandpaper, moving the sandpaper in small, circular motions. This will allow the spackle to become even more flush with the wall.
Vacuum the wall again using the shop vacuum to remove any debris and dust.
Fill a paint tray with latex paint, then coat a paint roller in the paint.
Apply three coats of latex wall paint over the repaired wall using the roller, allowing the paint to dry for 8 hours in between each layer.