Now cut some notches in the wallpaper following along the path of the archway. Be sure to cut the paper as closely to the edge as you can while avoiding the pitfall of cutting into that part of the wallpaper that will ultimately be on the wall itself. Word of advice on wallpapering an archway in this fashion: cut more notches in correspondence to the tightness of your arch. A loosely arching curve means fewer notches and a constricted arch means lots of notches.
Press the flaps hanging down after you have cut notches into the wallpaper against the underside of the archway. When one of the rooms adjacent to your archway is also going to be wallpapered, you should wrap the wallpaper around the edge of the arch, too. Now get out a ruler or tape measure and take a measurement of the thickness of the archway. Cut two strips of wallpaper so that they are 1/4th of an inch less than the thickness of the archway. The total measurement of the two strips should equal the distance around the interior section of the archway. Join the strips of wallpaper together. The most aesthetically pleasing result will be accomplished by joining them near the center of the archway.
Apply some vinyl-to-vinyl adhesive to the back of the strip of wallpaper and line it up along the inside of the arch. Keep a space of about 1/8th of an inch at each edge and the smooth over the strip of paper using a brush. A moistened sponge will take care of any paste that oozes out and then you are done. Just like that you have beaten back the demon of an archway that needs to be wallpapered.