Brush paint on several small areas of the wallpaper -- including near the seams -- and let the paint dry. Paint may cause old wallpaper to slide off the wall or bubble up. If this is the case, you will need to remove the wallpaper. If the paint dries smooth and the paper stays on the wall, however, continue with the remaining steps.
Wipe the wallpaper clean with a damp sponge. Starting with a clean surface will help the paint stick better. Remove switch plates and outlet covers and protect trim and baseboards with painter's tape.
Move your bare hands over the wallpaper and feel for any imperfections -- such as dents or scratches -- in the wallpaper. Repair any imperfections with spackle, let it dry and then sand it smooth with a fine piece of sandpaper. Use a damp sponge to wipe off the dust created when sanding the spackle. Let the wallpaper dry.
Be sure your primer is well-stirred. Apply a coat of primer using a paintbrush around the edges and around things like outlets and light fixtures. If you have big expanses of wall, pour primer into a tray and use a roller on the open areas. Apply the primer in steady, even strokes. Let the primer dry for 24 hours.
Stir the paint and paint with a brush around the edges of the room as you did with the primer. Fill in open wall areas using a fresh paint roller and paint tray. Apply the paint to the walls in even and steady strokes.
Let the paint dry for at least 24 hours, and check closely to be sure it has covered the wallpaper. Reattach the switch plates and outlet covers. Remove the painter's tape.