Some wallpaper are simply a pain and will take forever to remove, this guide will help you to make it as speedy as possible.
Plastic and paper faced wallpaper should be peeled off first leaving a thin layer of the backing that has the glue on it. Use a spray bottle, if you have a big weed sprayer bottle that works even better. Use lots of water, put down drop cloths or towels if your worried about damaging the floor.
Peel away the glued pieces after the water has done its job, now you should be left with a clean but somewhat tacky wall. Remove the glue residue with some TSP (trisodium phosphate) or a wallpaper glue removing product.
It's a good idea to prime the wall first, then apply your paint.