Scrape away loose paint from the ceiling that's peeling. Use a scraper for this job, or 100-grit sandpaper. This may be a big undertaking, but it is necessary, as new finish won't stick to peeling paint.
Apply a thin layer of patching material to any small cracks in the ceiling using a putty knife. Allow the material to dry and sand smooth with 220-grit sandpaper. Sand around the edges to ensure they're smooth with the rest of the ceiling.
Screw plaster washers through the ceiling, for larger cracks, and into the wood lath above it, all around the cracks. Apply joint compound with a putty knife, covering the washers. Press a piece of screen material into the compound and remove, then smooth the compound with a trowel. Smooth with 220-grit sandpaper after the compound has dried for 24 hours. Repeat if necessary.
Wipe the repairs with a damp sponge to remove any debris from sanding. Finish the ceiling as desired.