Cover the floor with a drop cloth before working on the ceiling. Scrape away any damaged ceiling texture around the repair area with a putty knife.
Use a sander with sandpaper to sand the edges around the damaged area.
Take the putty knife and apply a small amount of drywall compound on the area. Fill it with a smooth coat of this compound and then let it dry.
Reuse the sander on the area until you have a smooth surface. If it was a stain due to water damage then apply stain sealer over the area and then let it dry. This can prevent bleed through problems in the future.
Re-texture the area by using a spray texture repair kit. There are many kits available such as acoustic (popcorn effect), orange peel, splatter and knock-down that should match your ceiling texture. Follow the kit instructions and first practice to achieve the desired effect; then begin to work on the ceiling.
Recreate a splotchy-style texture look by applying drywall compound on the area and then use texturing brushes to achieve a match to the surrounding ceiling texture. You can use this method if you are unable to use a kit for this particular texture style.
Repaint the repaired area to match the rest of the ceiling. It might be necessary to repaint the entire ceiling to ensure a perfect match.