Climb up to the damaged area and use your putty knife to scrape off all the damaged stucco and surrounding area. Get it flat and smooth.
Mix your stucco in a bucket with water, using your drill and mixing bar. Follow the instructions on the packaging until you've made a small batch that has the consistency of thick mud.
Trowel the stucco onto the damaged area, using your concrete trowel. Make it about 1/4 inch to 1/2 inch thick on the ceiling.
Use your trowel to work the stucco in the same pattern as the rest of the stucco on the ceiling. Variations include swirling the stucco with the trowel, or pressing the trowel flat against the stucco and pulling straight down to create peaks.
Let the stucco cure for at least 48 hours. Touch-up paint with a thick roller and ceiling paint.