To remove wallpaper borders from drywall involves special care. The outer paper layer of drywall is particularly susceptible to water damage and scrapes.
Step 1 - Dry Removal
It is always best to try to remove the wallpaper dry first. Peel up a layer at the corner of the room with a putty knife and try to pull it back at an angle. Peel gently or you will rip off chunks of drywall paper. If the wallpaper yields easily with a few nudges from the putty knife, continue until it is fully removed.
Step 2 - Permeating the Surface
If the paper is firmly stuck on and is not porous, such as some borders having a vinyl surface, you will need to score the paper lightly using a circular wallpaper puncturing tool or by sanding before proceeding.
Step 3 - Softening the Wallpaper
Spray the wallpaper with enzyme-based wallpaper remover, or at the very least with a homemade solution of fabric softener and water. Take care to avoid over-wetting the wallpaper, since it can soak the paper covering the drywall underneath. Only spray an area that you will be able to scrape off in a ten minute time period.
Step 4 - Scraping It Off
Scrape the softened wallpaper from the drywall, being careful to avoid gouging the drywall.
Step 5 - Repairing Any Damage
Even with your best efforts, the drywall may still be damaged in a few places after removal. Coat the damaged paper areas with shellac and let dry. Patch with drywall compound and sand until even.