If repainting or re-wallpapering a room, you're going to have to remove any existing wallpaper or other wall coverings. It may be tempting to just tear these off, but doing so can cause damage to the drywall beneath. Going about things the right way may take a little longer up front, but should save you from having to do fix drywall damaged by hasty wallpaper removal.
Wallpaper Removal
Sometimes wallpaper removal actually is as simple as just peeling it off. Start at the corner of a strip, and use a putty knife to lift the corner away from the wall. Gently pull the paper away from the wall at a shallow angle (pulling it straight away will most likely cause damage to the wall.) If the paper pulls away without tearing the surface of the underlying drywall, keep peeling. If it does start to tear the drywall, stop peeling and move on to the next step.
If the paper won't just peel up, you'll need to use something to dissolve the glue holding it in place. Get a wallpaper removal solution from your local hardware store. Mix it into a spray bottle with some hot water and spray a test area. Allow the solution to soak in for about 15 minutes; the paper should come off pretty easily at this point. However, if you're dealing with non-porous wallpaper, the solution won't soak in and, therefore, won't work. If this is the case, score the surface of the wallpaper before applying the solution. This can be done with a scarifying tool or coarse sand paper. If the solution seems to be working on your test section, move on to the rest of the wallpaper.
Unfortunately, if the surface of the wall was not prepared properly when the wallpaper was put up, it may be impossible to remove the paper without damaging the wall. If this is the case, your best option is to put new wallpaper right over the old.
Other Wall Coverings
You might have other types of wall coverings to deal with besides regular wallpaper: commercial vinyl, felt, suede, foil, and many more. Thankfully, the removal process for all of these is generally the same as it is for standard wallpaper. First, try to dry strip it the wall covering as described above. Some wall coverings, like commercial vinyl, will most likely come right off. Felt or suede wall coverings usually peel away from their backings. Then, all you have to do is use a wallpaper-removing solution, as described above, to get the backing off the wall.
Some wall coverings have a layer of waterproof paper between them and their backings. These will need to be scored in order for the wallpaper-removing solution to be able to work.
Removing wallpaper and wall coverings really isn't that difficult a task. As long as you have a wallpaper-removing solution and some way to score the paper, you should be in good shape. Once the paper is down, you can move on to your next project: putting up new wallpaper or painting your walls!