Check the ceiling for asbestos if your house is more than 25 years old; have a licensed asbestos-abatement contractor do the work. If your ceiling tests positive, you will probably have to have a new ceiling installed. If there is not asbestos, proceed to the next step.
Put on a pair of safety glasses and a dust mask. Position a ladder beneath the crack if you need help to reach it. Work at a height from which you can comfortably reach the cracked area, but do not stand as far up as the top step -- it's very dangerous.
Scrape away any loose ceiling texture material from around the crack. Use a small trowel or a putty knife to remove the ceiling texture. Avoid standing directly under the area, so that the dust and debris do not fall on you.
Dip the putty knife into a container of joint compound. Spread the joint compound over the crack, filling the entire cavity as you go. Allow the joint compoud to dry before proceeding.
Sand any excess joint compound off of the ceiling, until the joint compound is even with the surface of the ceiling.
Apply a coat of textured ceiling mix over the crack area. Textured ceiling mix is available as a dry mix that you combine with water, and also as a spray on material. Allow the mix to dry before proceeding.
Paint the area in a color that matches your ceiling. Apply a second coat if you can see through the first coat after it dries.