Is this a plaster or drywall ceiling?

Did the ceiling get wet/damp sometime in it's life? Has this been fixed?

plaster - and no it didn't get wet. The house was built in 1921 - so maybe too many layers of paint?

You will need to scrape and sand to remove the loose, flaking and peeling paint. The prime will need to be a 100% acrylic primer so as to adhear to the plaster better as a regular latex primer which will not do anywhere near as good a job. This type of primer will often be called an undercoater, but the people at the paint store will be able to guide you in the right direction. It is your choice as to if you want to skim out the rough edges or not. The finish paint should be one made just for ceilings as they dry flatter and don't show up the rough areas as bad as a regular wall paint will.

Hope this helps out.

I have to paint my dining room and there was water damage. I am told the previous owners fix and they did put on a new roof. What do I do to that area that was affected by the water?

Is it plaster or drywall?