Lay down drop cloths to protect flooring and any furniture in your work area.
Mix warm water and a cup of trisodium phosphate in a bucket. Scrub the wall thoroughly with the TSP and a sponge to remove dirt and oils from the surface. Rinse the walls with clean water and a sponge. Allow the walls to dry for a couple of hours.
Repair sections of the wallpaper that are not lying flat on the wall. Use a small tub of wallpaper glue to reseal problem areas.
Cut in around the ceiling, floor and any windows with a good quality primer using a 2-inch paintbrush. If you are not confident of your cutting-in skills, use painter's tape to tape the edges of the ceiling, floor and windows to prevent getting primer on them.
Pour the primer into a paint roller pan and install a roller onto an applicator. Roll on the primer over the wallpaper starting at one corner of the wall and working your way across to the other side. Apply a thick, even coat. Allow the primer to dry for 24 hours before painting.