To remove peeling paint from your drywall scrape as much off as you can and then use a sander either a power sander or a manual sander and sand the drywall down to get a smooth surface.
After you've remove the peeling paint from the drywall and then sanded it down you can then add some primer to the drywall and then either a few hours later or the next day you can repaint the drywall with a new coat of paint.
You might want to add a second coat of paint to the drywall the next day to get a nicer look and I prefer to use paint rollers instead of paint brushes to get a nicer paint finish.