When walls are covered with wallpaper, the best thing to do is remove it before you paint. The problem with removing wallpaper is that it can be extremely difficult to take off the walls, which is usually because the walls have not been primed or sized prior to the wallpaper installation. Trying to remove this paper results in damaged walls that you must repair before you can paint. The solution is to paint over the paper, which is not a problem as long as the wallpaper is adhered tightly to the walls.
Examine the wallpaper for loose seams and air pockets. Use a putty knife to scrape along the seams to see if the seams will lift. You must glue all loose seams back down. Cut air pockets open with a thin wallpaper blade. Apply paste to the back of the wallpaper, and smooth it down.
Caulk across the top of the wallpaper where it meets the ceiling and at the bottom where the wallpaper meets the baseboard. Caulking eliminates the wallpaper line all the way around the ceiling and closes gaps between the baseboards and the wall. You will create a professional appearance by caulking.
Allow the caulking and glue repairs to dry overnight. Priming on top of wet caulking and glue causes the seams to lift and the caulking to crack.
Tape the edges of doorjambs and baseboards with painter's tape. Use a drywall knife or an edger to cut in around the ceiling. This step will eliminate the need to tape around the ceiling.
Remove all of the light switch cover plates and outlet cover plates with a flathead screwdriver.
Hold a drywall knife with the blade touching the seam between the wall and the ceiling. Start priming 2 inches below the drywall knife and work up towards the drywall knife to keep paint from flowing under the blade. Wipe the blade often with a wet rag. Roll a coat of primer on the wall when you have finished cutting it in.
Repeat step 6 on the remaining walls. Allow the primer to dry overnight before you paint it.
Examine all of the walls for bubbles. Weak areas will come loose from the wall, which you must repair. Pull off the weak areas, and prime everywhere you pull off the paper. Allow the primer to dry, and apply a smooth coat of drywall compound to those areas. Allow the drywall compound to dry overnight.
Sand all of the repaired areas with 100-grit drywall sandpaper. These areas must be sanded completely smooth and level with the surrounding wall area. Thick repairs will appear as humps on the wall when it is painted.
Prime the repairs, let them dry and cover coat the walls with paint. Allow the paint to dry for the amount of time recommended by the manufacturer. Apply a second coat of paint if needed.