Sand the ceiling with 100-grit sandpaper to smooth as much of the texture as possible. Wipe the ceiling with a tack cloth to remove the sanding dust.
Apply drywall primer to the ceiling using a sponge roller with a thick nap. The thick nap will work the paint between the rough textures on the ceiling and fill them in. Allow the primer to cure according to the package directions, then apply a second coat.
Apply a flat, latex paint over the primer using a sponge roller. Flat paint is thicker and hides flaws better so it's a superior choice to gloss paint. Allow it to cure and apply a second coat.