If the damage is small, then repairing a popcorn ceiling is very easy, but if it is big, then, you should ask for professional help. Before you start with the repairs, you need to gather basic tools like a ladder, painters tape, scraper, knife, joint compound, primer, roller, and paint.
It is important to mask off the ceiling area around the damaged patch. Make sure to cover all fixtures like lamps, ceiling fans, cameras, etc. properly. Cover the floor with plastic sheets and secure them with painters tape.
If the ceiling patch to be repaired is near a wall, cover the wall as well to avoid damaging its look due to products that might accidentally get sprayed on it. Don't forget to wear safety gear, like goggles, gloves, and a cap.
Sand the primed surface to prepare it for the paint job. Since you are working on small holes and cracks, you need to use a roller or spray to complete the paint job. While painting this patch, make sure that the texture matches that of the rest of the wall. Finish the task by painting this repaired part with matching paint colors.
If the holes and cracks are large, then, you need to carry out the same procedure. But, before you start painting the ceiling, you need to sand the primer, and then add texture to the wall. Use a roller or a napkin for this procedure. Once the textured area has dried properly, complete the repair work by painting over it.
When you start with the repair, if you feel that you will not be able to do it yourself, ask your friends or family to help you. If you feel that the damaged area is too large, then the safest option for you will be to get a professional to do the job.