If the border is loose or torn, it may be easy to simply peel the border away. Determine any products or special tools you may require, such as chemicals or special scrapers, to facilitate the process. You may use a hair dryer to loosen the adhesive, or a spray mister to lightly moisten the wall to make it easier to scrape. If it is not possible to remove all of the border, you may opt to paint over it.
In order to achieve a smooth finish, you should take the time to fully prepare the surface. Remove loose paper by gently pulling it away from the wall. Any paper that cannot be removed should be firmly glued down. Use joint compound to patch any holes in the wall, then apply it to the entire border. A fine sandpaper will smooth away irregularities and produce a seamless transition between border and wall. Remove any dust with a damp cloth.
Since most adhesives on wallpapers are water based, it is best to use an oil-based primer to prevent moisture from absorbing through the paper and releasing the glue. Darker wallpaper borders require more coats of primer to cover well. Add tint to the primer as close as possible to the color of the paint you are going to use on the walls. Apply at least two coats to seal the border, allowing it to dry completely between coats.
The border will take longer to dry because it absorbs the primer, so be absolutely certain that the primer is dry before beginning to paint. Choose high-quality paint for the best coverage and stir it well before you use it on the wall. Apply two coats of a flat or satin sheen paint to hide any imperfections. If you have prepared the surface and primed it well, the border should be invisible.