Cover your working area with an old bed sheet to prevent any paint or debris from damaging your floor.
Scrape away the material in and around the cracks in your ceiling. Use light sandpaper to smooth out the edges around the repair area.
Apply drywall putty to a putty knife or tool and spread it into the crack, smoothing it out as best you can. Let the putty dry at least an hour.
Use the sandpaper to smooth out the putty and make the entire repair area smooth and level with the rest of the ceiling.
Add texture that matches the rest of your ceiling with a texture repair kit. The right repair kit should be easy to find by looking at the picture on the front of the kit, and making sure it is similar to your ceiling.
Paint the newly applied textured repair with ceiling paint that matches the rest of your ceiling. You may have to paint the rest of the ceiling with the new paint for it to match.