1. Prepare the right tools.
First, gather the necessary tools. You will need wallpaper solvent, available at most home-improvement stores. A solvent you can make yourself that works well is hot water mixed with fabric softener. It is wise to have drop cloths or plastic sheeting to protect the area around the walls. You will need trisodium phosphate, spackling compound, sandpaper, a scraping tool or putty knife, a perforating tool and possibly a wallpaper steamer.
Remove all the face plates from electrical outlets and switches, telephone jacks, any picture hangers and anything else that is attached to the wall. Any electrical outlets should be covered with tape so no moisture gets in when you spray solvent on the walls. Cover the floor with drop cloths or plastic sheeting.
3. Test the stickiness.
At this point you will want to test the wallpaper adhesion to see how easy or difficult it is to remove. Some wallpapers will peel off easily while others are stuck to the wall. To test the difficulty of the peel, start at a corner or at a seam and try to peel the paper away. If it comes off easily, you won't need a steamer.
4. Perforate the paper to let solvent spread.
Even if the paper is peeling off easily, you still need to perforate the old wallpaper. A perforating tool is a roller with little spikes that punch holes in the paper. Don't press too hard so you don't damage the wall behind the paper. The little holes made by the tool allow the wallpaper solvent to penetrate and unglue the paper from the wall. If you are using your own hot water mixed with fabric softener, put this mixture in a spray bottle. Be sure the water is hot and mix a little at a time so you can keep remixing with very hot water.
5. A steamer can help.
If you have heavy or old paper that has been on the wall for a long time, you might need to rent a wallpaper steamer. This is a messy job, as there is steam and hot water dripping as you work. You might want to open a window to release some of the heat and steam. There should be instructions with the steamer.
Whether you use a solvent or the steam method, you will need to scrape the paper off the wall. Some of it will peel off, but some won't. So scraping is necessary. A wallpaper scraping tool or a putty knife will work. Be sure to get the wallpaper and the backing off the wall.
7. Spackle, then clean up ... and you're done!
It might be necessary to repair some parts of the wall, and usually spackling compound will do the trick. A little sandpapering might be necessary in some areas. Then all that is left is the cleanup. Here is where the trisodium phosphate comes in. Use a sponge to wipe down the walls.