Sanding wallpaper isn't the ideal way to prepare a wall for paint or new paper -- stripping it is a much better way. Some wallpaper sticks so well, however, that trying to strip it is futile. If the paper is thick, and the stripper doesn't penetrate even after scoring it with a wallpaper scorer, there's a better chance of making a mess by continuing your efforts than there is of creating a smooth substrate. Sanding -- not to remove the paper, but just to etch it -- is an easier and cleaner option in such a case.
Step 1
Wash the wall with a sponge and a solution of 1/2 cup trisodium phosphate per gallon of warm water. This is a strong detergent that will remove any oil or grease that can gum up the sandpaper. Let the wall dry overnight.
Step 2
Sand with 120- or 150-grit sandpaper. Coarser paper may scratch right through the wallpaper, while a finer grit won't abrade it sufficiently.
Step 3
Attach the paper to a pole sander and sand with vertical strokes. Apply enough pressure to dull the finish, but not enough to tear the paper. If the paper is already torn in places, sand enough to remove the loose paper and smooth the edges of the torn area.
Step 4
Change the sandpaper when the grit wears down or it becomes blocked with material. If the paper blocks frequently, wash the wall again before proceeding.
Step 5
Prime the wall with PVA primer after you're finished sanding. If there are torn areas in the wallpaper paper, apply a coat of joint compound to those areas and scrape it flat with a drywall knife. Let it dry, then apply a second coat and scrape it in the same way.
Step 6
Sand the joint compound patches with 120-grit sandpaper after the last coat dries. Feather the edges of the patches into the rest of the wall. Cover the patches with PVA primer.