Just like scraping off flaking old paint when going to repaint something like a window or fence. Scrape, remove loose pieces, patch, prime and paint. (At least what I would do but if an actual drywall expert weighs in go with their advice.)

I have cracks in my plaster ceiling but they can't be pushed back in like that. It's from foundation settling as the wife over the last 8 years has been doing yardwork changing the water penetration to the ground.

Good luck OP.

Edit: watched that YouTube link below. If that works that might be easier and less mess.