How do I fix my kitchen ceiling?
From what I see in your pics, you have a plaster ceiling that is failed. Usually water is the culprit for delaminating the scratch from the finish coats. 

You have two options to repair this.
First option is to remove all loose plaster down to the lathe and replace it with new plaster. This is not as easy as it may sound. Working with real plaster takes some skill and practice. Matching the original texture of the finish can be tricky.

Second option is to recoat the entire ceiling with a layer of 3/8" drywall. Although this may be a bit larger job, it will secure any loose, soon to fail plaster. The new drywall ceiling will be clean and smooth if taped properly and give many years of service. I have found that once a plaster ceiling starts to fail, it will usually continue to get worse.