Prepare the area for painting. Remove switch plate covers and window coverings, pull furniture out of the way, and protect the floor with drop cloths.
Wash the walls with a damp rag and mild detergent to remove surface grime and dust.
Tape the trim with painter's tape, unless you're going to paint it. Apply it to baseboards, door and window trim, pressing it down firmly with your finger to prevent primer and paint from seeping underneath.
Check seams and corners for loose wallpaper and glue it down with wallpaper seam paste. This typically comes in a small tube. Insert the nozzle under the loose paper, apply a liberal amount of paste and smooth the paper down with a dry rag. Allow it to dry for about an hour.
Prime the walls with fast-drying oil-based or tinted shellac primer. Don't use water-based primer; it will tend to loosen the wallpaper. Use a 2- or 3-inch brush for the edges, and roll the walls with the primer using a foam roller cover. Dispose of the roller cover when finished; it's not worth the effort to clean it out with mineral spirits. Allow the primer to dry -- typically one to two hours.
Patch holes, dents and seams with joint compound. Use an 8- or 9-inch drywall knife to apply a wide swath of compound over each seam. Allow it to dry, then sand all patched areas with a drywall sander or sanding sponge.
Prime over the repairs with water-based primer. While that's drying, apply a bead of caulking around the top of the wall where it meets the ceiling; there's usually a slight visible seam there. Smooth the caulk with your finger as you go and allow it to dry for about four hours.
Paint the walls with two coats of interior latex or acrylic paint. Cut in all the edges with a brush first, then roll the walls.
Remove the masking tape after the walls have dried for about four hours. If you remove it too soon, you may pull some of the fresh paint away from the wall.