The most effective and long lasting method of adhearing a border to existing wallpaper is to purchase a specifically designed Border Adhesive or a Recommended ready mixed paste.
Decorative paper borders have a glue backing and will stick if you follow manufacturer instructions for applying them. Make sure the wallpaper base is clean and in good condition.
Get a wallpaper glue from your local hardware store. Places like Lowe's and Home Depot also carry them. Brush it on the wallpaper and stick it to the wall.