Painting over Wallpaper
The best route is to use proper wallpaper stripping techniques first. This will tell you if the wallpaper can be stripped successfully or not. Sometimes painting over wallpaper is preferred. Where wallpaper is adhered to unprepared drywall, this can be the only way to go.
Before deciding to paint over wallpaper, you should always attempt to strip the existing paper first. If after a valid, dedicated attempt at paper removal, it either causes wall damage or just refuses to come off, then you may take the steps for painting. This decision should not be taken lightly! Wallpaper stripping over a properly prepared surface is actually easy to do. Stripping painted over wallpaper can be the worst case scenario and will cause you or the future homeowner problems.
Preparation is the key to painting over wallpaper. Remove any loose paper areas first. Then apply joint compound to any nail holes, seam areas, or other damaged spots. Sand these areas smooth after proper curing time. The more time you spend filling holes, patching, smoothing, and sanding, the better your end result will be. Once you are finished your prep, close your eyes and rub your hand over the entire wall surface. Your hand will tell you where the errors are better than your eye. Without valiant efforts at preparation, it will look just like you painted over wallpaper. Then apply a good quality primer/sealer such as Scotch Paint's Draw-Tite, Zinsser's Gardz, Roman's Liquid Drywall, or Sherwin Williams' PrepRite Drywall Conditioner over the entire surface. Now your wall is 100% ready for paint or additional wallpaper.
All prices are in USD.