The first time I ever removed wallpaper from a room, the job was a snap. The paper was old and brittle, and the glue had lost its life. I sponged on a liquid wallpaper-remover and the paper practically threw itself into the trash can.
Things don't usually go that well. New papers in vinyl and foil are impermeable to liquid removers. So are ordinary papers that have been covered with paint. These problem papers call for special techniques.
First, spread plastic film on the floor (tape it to the baseboard). Then remove all switch and outlets plates and cover the fixtures with masking tape.
If the paper is one of the problem types, scuff it up by rubbing it with 50-grit sandpaper wrapped around a block. The idea is to cut through the waterproof surface so the remover can soak through. You may have to score the paper every few inches with a utility knife. Use only enough pressure to break through the surface film.
Now mix a batch of liquid wallpaper-remover and sponge the mixture onto the wall -- or better yet, spray it. It's important to wait for it to soak in. Once the paste is soft, start removing the paper. Some fabric-reinforced types are so strong you can often pull them off the wall, but most require scraping. Use a wide, flexible putty knife and dump the paper right into a large trash can. Some papers will not come off in a single operation. You will have to reapply the remover, let it work and scrape again. This is almost always the case when you're dealing with two or more layers.
If possible, have a helper follow along behind you. He or she can spray on a thin coat of water and scrub the wall with a plastic scouring pad. This will loosen the remaining traces of paste.
The final step is to squeegee the wall dry with an ordinary window squeegee. Clean up the mess, and let the room air out so any remaining moisture can evaporate.