It is neither practical nor economical to remove paint from an entire wall or room of wallpaper. The following directions and suggestions are appropriate for spot paint removal, or for patching smaller irreparable sections. That said, it is possible to clean new or older paint stains off of your existing wallpaper. This saves a great deal of money over the cost of repapering or repainting the entire room, and allows you a chance to spruce up the existing wallpaper.
If the paint is fresh, dab the area with a towel or sponge and warm water. As with a stain on carpet or cloth, dab—do not rub—as you want to lift the stain without pressing it into the fibers.
If the paint stain has dried, you can still have some luck removing it. Apply a liberal amount of rubbing alcohol to a cotton ball. Heavily dampen the affected area, and allow to sit for a minute or so. The paint should lift off when you apply a damp sponge. Repeat until you have removed all paint from the affected area. It is important to note, however, that you should always test a discreet spot for color fastness to ensure that you do not discolor the wallpaper.
The worst-case scenario is that, for whatever reason, you are unable to remove the stain, but are still committed to the wallpaper. In this case, your only option, short of repapering the entire room or wall, is to replace the damaged portion of the paper. With an X-Acto knife and a surplus roll of your paper, identify the correct portion of the pattern and cut the desired amount for your patch. Using this as a template, hold it against the wall, and with your pencil, trace around the edges. Cut the outlined portion away from the wall, taking great care not to overcut. Apply your patch as you would apply the wallpaper (e.g., with paste or by dampening).