Wear a protective mask and glasses so you don't end up with paint dust and flecks in your eyes or mouth.
Use a wide putty knife to scrape all of the peeling paint from the surface; now you want to remove all that you can so that your repair will stick.
Once all of the peeling paint is removed, wipe the area down with a damp cloth to remove residue and dirt. Let it dry completely.
Use that same putty knife to cover the area where you removed the paint with some lightweight spackle. Level it so that it's even with the surrounding paint.
Let the spackle dry and then sand any rough areas and reapply the spackle if necessary.
Once you're happy with the repair, prime the area and then repaint to cover the repair and no one will be any the wiser. I'm Mrs. Fixit and it's just that simple.