How do we repair a wall that was damaged in the removal of wallpaper?

Add a skim coat of sheetrock joint compound over the damage. Then it can be textured if desired and repainted.

i just had to go through the same thing. I filled the damaged areas with spackle. I sanded when it was dry. Then I primed over the spackled areas otherwise you see a shadow when you paint.

You probably want to prime the area if there is a lot of repair.

Exactly as Tricia suggests. Use no shrink drywall patching compound to repair the damage. Sand smooth, Prime with Kilz primer, and paint.

What is your wall made of? Depending on that there are options. Personally, I don't always like to use patching compounds, and depending on the extension that was damaged I might recommend that you plaster it completely to get a smooth surface.

can you provide some pictures ?

Drywall repair spackle could be used and sanded level if your walls are indeed drywall and smoothly finished.

Some homes do have a textured finishes that could prove more challenging.

If it was wallpapered I am assuming it was probably a plain drywall surface. Best wishes with your wall rehab.