Seal the surface, apply beadboard right on top of the wallpaper with a few nails and some construction adhesive, and preserve some of the old character of the surface.
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Sure up the surface of the old wall by painting over it with an oil-based primer sealer on a roller to give the beadboard something solid to stick to and to prevent the wallpaper colors from bleeding through on any areas you paint. Let the sealer dry thoroughly for the time recommended by the manufacturers before trying to install any beadboard.
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Find the highest place on the floor and then measure up from there to where you want to hand your beadboard. Mark a straight horizontal line at that point and snap a chalk line to get a straight line, especially if the house is old with slightly uneven walls and floors.
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Remove the baseboard molding so installing the beadboard can start at the floor level. Cut through the painted seams with a utility knife and then pry it up carefully with a five-in-one scraper and a hammer so you can replace it after the beadboard installation. Tap out the old nails and set the trim aside.
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Install the beadboard sheets by applying a lines of construction adhesive every six inches. Nail each panel in place at each corner and in the center of the top edge. Measure and then cut the pieces to fit, marking out holes for receptacles.
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Reapply the baseboard and then apply the top cap molding using trim nails. Caulk any seams with paintable latex caulk.
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Paint the walls and the beadboard as desired.