Lay a drop cloth under the area you will be working on and place a stepladder in the center. Scrape the area around the crack with a dry trowel to remove any flaky material.
Scoop 2 cups of drywall mud into a drywall pan with a trowel. Smear a small portion of drywall mud over a small section of the crack, repeating the process until the entire crack is covered.
Determine the length of drywall tape required to cover the ceiling crack using a tape measure, and cut the amount from the roll of drywall tape. Press the tape into the drywall mud with your fingers, starting at the center and working to the ends. Gently smooth out with a trowel and wipe off excess mud on the edge of mud pan, making sure you have a smooth finish with no bubbles.
Allow the tape and mud to dry eight to 12 hours in temperatures between 50 and 60 degrees. Higher or lower temperatures will take longer to dry.
Touch the drywall mud to be sure it is completely dry. Gently sand off any rough areas with a sanding sponge.
Apply a second coat of drywall mud over the taped area using a clean trowel, smoothing it to remove any bubbles or rough areas. Allow mud to dry completely before painting over it.