Start by stripping the outer face off of the wallpaper, sometimes this is a vinyl coating and other times, it is just a dense layer of paper.  This should leave only the backing material and glue.  Prepare a wallpaper stripping solution consisting of water and a little dishwashing detergent.  Wallpaper stripping solution should be sponged on the backing material and allowed to soak (re-wetting as necessary) for at least 10 minutes.  A cheap garden-type sprayer will tremendously speed up the soaking process.  Attempt to remove the backing material with a wallpaper scraping tool or alternately any flat bladed tool such as a wide putty knife.  If this fails, re-wet the backing and allow to soak longer.  The more you soak, the easier the job.

If the above stripping solution is not working well enough, you may also try a solution of 2 parts water to 1 part white vinegar and use the same technique.  This stripping solution is only effective against wallpaper installed using wheat or starch based wallpaper adhesives.  If the adhesive is unknown, use one of the below listed strippers.

Obtain some Safe and Simple online, or Dif  from your local home improvement store, and follow the bottle's directions to remove the remaining backing material.

If you plan on painting the area you just stripped, you must ensure that all the glue behind the backing is removed.  To tell if there is still glue remaining, wet the wall and feel it.  Any slimy areas mean there is glue left over.  To remove any remaining glue, mix 2 tablespoons of liquid fabric softener into a gallon of water and scrub.  You must also carefully rinse the entire wall surface so there are no traces of paste or wallpaper stripper remaining behind before you paint.

If your vinyl/dense paper facing does not want to peel off the backing, you may try to dry peel it off the wall which may or may not cause wall damage.  You can also obtain a wallpaper scoring tool, such as the Paper Tiger, to score the paper and perform the above steps for removal.  Paper scoring tools can damage the drywall underneath the wallpaper, but are gentler on plaster walls.  Ensure you read the directions on the package for complete instructions, but a good rule of thumb is to let the tool do the work.  Additional lateral pressure will cause undue damage to the wall surface.  An alternate method is to use a razor to score a series of Xs into the wallpaper surface.  This requires a careful touch as to not damage the underlying wall surface.  In some cases, the scoring and soaking steps will promote or enhance the stripping of the facing material, so after this step, attempt to remove the facing material again.  If still no success, you will have to perform repetitive score, soak, and strip steps to remove your wallpaper.