If you want to re-wallpaper a wall, far and away the best option is to remove the old paper. If you don’t want to go to the trouble, or the old paper is difficult to remove, you can attempt it if the old paper is a single, smooth layer. Be aware, however, that several mishaps can occur, so it is best to test the new paper in an inconspicuous location before tackling the whole wall.
A lot of your success will depend on the kind of new paper you choose and the nature of your old paper, so consult with your retailer before making any purchase. For example, the old paper may come loose when it is moistened with the paste for the new paper, making it impossible to achieve a smooth surface. Or, with the moisture from the paste, the ink from the old paper may bleed through, indicating the need for a primer-sealer. If the old paper is vinyl, it may not accept the adhesive for the new paper; in this case, first apply a vinyl-to-vinyl primer, which will not only ensure adhesion of the new paper but also serve as a mildewcide.
If you have tested a small area and are confident of your ultimate results, start by preparing the wall. Repaste any loose areas, sand any rough spots and all seams, and then spackle any dents or nicks. Using ammonia and water or a solution of TSP (or a non-phosphate-based alternative), wash the wall from bottom to top and allow it to dry overnight.