Professional painters are almost unanimous in their recommendation to remove wallpaper rather than paint over it, but sometimes leaving the wallpaper is the lesser of two evils. Removal can be messy, and it's all too possible to damage the wall. If the paper is in relatively good condition, with few bubbles or lifting seams, you can use the same technique to create a smooth, paintable wall that you would use for a textured wall.
Before applying any type of paint over wallpaper, it's vital to ensure that it's well adhered to the wall. Assess its condition by running a drywall knife lightly over the entire wall. Any spot that you can easily work out or press in with the knife is a problem area, and the paper in that area either has to be glued to the wall or scraped off with a utility knife. Dig the corner of the knife into small bubbles to puncture them, then scrape off the loose paper. If the paper comes off with little effort, and small voids quickly turn into large ones, you should reconsider your decision to paint over the wallpaper.
Sealing and Priming
You need to seal the wallpaper seams to keep the moisture in the products you spread on the wall from seeping behind the paper and loosening the glue. Do this with a shellac-based, stain-blocking primer. Before you spread the primer, wash off any mildew with a solution of 1/2 cup chlorine bleach per gallon of water. Dry the wallpaper with a soft cloth. Paint the primer along the seams with a paintbrush, then cut in the edges of the wall and roll the primer over the entire wall with a medium nap roller. Wear a respirator during this procedure, and keep the room well ventilated.
Drywall Mud Skim Coat
After priming the wall, skim coat it with drywall joint compound to hide the wallpaper seams, as well as all the bubbles you repaired. Cover the floors and furniture with plastic sheeting, as this can be a messy procedure. Premixed mud has just the right consistency for this job -- trowel it on with a 6-inch drywall knife and scrape it flat using the same knife. Even though the idea is to leave a very thin layer on the wall, you'll probably need two applications. Sand the final coat with a pole sander and 150-grit sandpaper when it dries. Wear a dust mask while sanding.
Painting the Wall
After you've sanded the mud, you need to prime it again, but this time, use poly vinyl acetate drywall primer. It seals the mud and prevents the wall paint from blotching. You're now ready to paint -- and at this point -- you can treat the wall just like any other wall by brushing and rolling two coats of latex-based wall paint over it. Use a synthetic-bristle brush to cut in around the edges of the wall and around trim, and then immediately roll the wall while the cut-in paint is still wet using a medium-nap roller.