How do you fix plasterboard with damaged paper?

[#1]

If the paper face has been pulled off your Gyprock sheets, you should start by scraping away any of the flaking paint that is no longer bonded to the surface beneath. Once the loose, flaking paint has been removed, you'll need to apply a skim coat of plaster to the areas where the paper has been pulled off.

This can be done with a 250mm Taping Knife and some Easy-Finish Topping Compound. Apply a thin skim coat, doing your best to avoid leave lines or heavy edges, to all areas where the paper has been removed. 

Once dry, you will need to sand it smooth using a combination of a 120 Grit Angled Sanding Sponge and a Plaster Hand Sander.

Once smooth, you can apply a coat of primer before painting with your choice of interior paint.

You might like to have a look at How to paint like a professional for some further guidance. - JacobZ