Put your protective gear on. No skin should be exposed during the removal process. You will need to wear safety goggles, an approved respirator, coveralls and gloves. You will need to dispose of the coveralls when you are done with this project.
Remove all furniture from the room. In fact, everything in the room will need to be removed. Ideally, if you are replacing the carpet in the room as well, this should be pulled up before you begin.
Put drop cloths down. Cover the entire floor in plastic drop cloths. Tape the cloths up so that dust cannot fall down between the wall and coverings. Doorways should be covered in plastic and taped off, and all vents in the room must be covered as well.
Begin scraping the wallpaper off. Wetting the wallpaper down will reduce the chances for airborne dust. Fill a spray bottle with a mixture of hot water and liquid fabric softener. This will help release the adhesive on the wallpaper and make the job easier. Use a 4-inch drywall knife and begin scraping away the paper and the paint.
Clean up all the dust. Keep your protective gear on and use a shop vac to vacuum all the dust in the room. Dispose of all the paint chips and wallpaper scraps in sturdy plastic bags and take them to your local landfill -- they will have a place for this material.