You can paint over wallpaper, but …
Q: Is it possible to paint over wallpaper that is on very well? If so, what is the best procedure? — A reader via e-mail
A: It’s possible, though not advisable. Paint doesn’t always adhere well to the paper, especially if it’s glossy, and very colorful or highly textured paper will often show through the paint. I’m not saying you can’t do it, though! I painted over rose-striped wallpaper in one of my first apartments, without any preparation, and never had a problem. So, test the paint color of your choice in a corner of the wall, let it dry and see how it looks.
If the wallpaper is not ripped or peeling away, you can paint over it without much trouble. I recommend lightly sanding the entire surface, wiping it clean with a damp cloth, and letting it dry for a day or so. Then, put a coat of sealing primer over the wallpaper. This will keep the paint from soaking into the paper (reducing the amount of paint needed for the job) and prevent old stains, moisture or air from bleeding through. Primer also provides an evenly colored surface to paint on. Once it’s dry, paint away.
What if the wallpaper is ripped or the edges are peeling away? If removing all of it is a pain, patch the ripped area with a spare piece of wallpaper to ensure an even wall surface, and glue the edges back in place. Sand the ripped edges lightly, and if necessary, apply spackling compound over the edges, feathering the compound to create a smooth surface. Missing patches of paper and ripped edges will show up as clear imperfections on your newly painted wall.
The toughest scenario is wallpaper that is more than half removed, albeit in strips, dribs and drabs (because it is stuck so well to the wall that conventional removal is almost impossible). In this case, don’t paint until every method of wallpaper removal has been tried, including steaming the glue away or using chemical solvents. (These tools are available in the wallpaper and paint sections of your home-improvement store.) If there are globs of wallpaper left on the surface, they will be seen through the paint as odd bumps and lumps, no matter how much sanding and priming you do.