Inspect the wallpaper for any raised or torn pieces around the joints where two pieces of wallpaper butt together. If you locate any, glue the pieces back to the wall by inserting a small amount of wallpaper adhesive behind the paper. Use a wallpaper roller to secure the wallpaper to the wall.
Inspect the wallpaper for any missing pieces or gaps between the joints. Place a small amount of drywall compound over the damaged surfaces with a putty knife. Work to keep the compound flat on the wall. Allow 24 hours for the drywall compound to dry and then use a sanding block to lightly sand the compound until it is flush with the wall.
Clean the surface of the wallpaper with warm, soapy water. Do not get the rag excessively wet; wring it out thoroughly before cleaning the wall. Water can weaken the adhesive. Wait 24 hours before painting.
Use painter's tape to cover all areas you do not want to paint, remove all outlets and register vents, and then lay down drop cloths to protect the floor.
Apply a thin coat of primer to the wall with a paint roller. Use a "W" pattern with the roller to ensure adequate coverage. Apply two thin coats as opposed to one heavy coat. A heavy coat could cause the adhesive to weaken as it goes through the paper. Allow adequate drying time between coats. Follow the drying times listed on the primer container.
Apply a thin coat of paint to the wall, using the same "W" pattern you used with the primer. Again, apply two to three light coats as opposed to one heavy coat.