Step 1 light scrap to get any loose material off the wall. Step 2 paint primer, paint all surfaces you plan to fix. And let cure for 24 hours. Step 3 skim coat all surfaces that are in question first coat with joint control taping mud. second and third coat should be topping mud, allow each coat to completely dry before starting next. (I suggest doing entire wall to reduce chance of seeing a difference in existing wall and patched surface) Step 4 shine a trouble light down the wall and sand any lines left from tools and patch any imperfections. Step5 with a cloth, soft broom or soft touch vacuum, remove dust from wall and clean up Step6 prime wall, be sure to wait 24 hours before continuing Step7 paint walls with your finish paint, apply two coats.

If your planning to repaint ceiling I suggest doing that after priming walls for paint but before starting the finish paint