Wall-covering condition is dependent on the construction underlying the visible wall. On the surface you may see simple paint, variety of coatings, previous wallpaper, plasters with lathing penetrating an old surface, etc. New installation will be complicated by previous materials covering the wall and by type of wallpaper used to cover your wall (e.g., plastic, fabric, etc.)
Your end installation “begins” with assessing the existing covering. If it is drywall or simple paint, there is no major preparation needed, just “sizing” (i.e. “sealing” the wall so that the new wallpaper does not integrate with the wall material, making it difficult or impossible to remove without damaging the wall surface).
If the wall has textured paint or textured coating, you may need to resurface the wall or remove that coating before you get to re-sizing the wall prior to your wallpaper installation. If the existing coating was applied without sizing, give up on removing it and begin leveling the surface with sandpaper. For some textures you may have to add drywall compound or spackle to level the wall surface before wallpaper application.
If you have “just” wallpaper, determine the quality of the paper or non-paper material and check to see if it is readily removed. If that wallpaper was installed without a sizing layer before its installation and it sits atop light plaster or wallboard, you have some decisions to make. Removal will cause major problems because the surface of the wall beneath the paper will be made irregular in the removal process requiring considerable time and energy to level the wall. A textured wall paper or fabric paper might be a simpler solution, but you must do a layer of sizing over the existing wall covering to assure that “new” wallpaper may be “removable” in the future.
If your wall is damaged by small holes in the wall, “spackle” the holes with a plaster or plastic type filler. For larger holes, repair the holes and then spackle the repair and sand or level as appropriate.
The kind of wall work necessary prior to installation will determine the materials you choose. For walls with removable paper, you will need to “strip” the paper. There are several strategies available, from applying water with a spray bottle to wetting the whole wall to applying special chemicals or steam and then scraping the paper off the wall. Home stores and paint stores abound with products for this phase, so do a little research.
Prepare the surface and level it. Little variations in surface may show through your ultimate wallpaper job, so spend time on this part of the task. Apply that sizing paint layer. There is a variety of products for this job. Put it on, and then move on to wallpaper.
Choose your wallpaper based on its ability to mask imperfections in your wall surface. Textured wallpaper may be preferred if you have lots of little indentations in the surface. If things are smooth, choose paper, plastic, or fabric covering. Choose a simple pattern unless you are willing to have lots of wastage as you match the patterns across your wall.
Research materials and patterns, but be prepared for “sticker shock.” You will find what you want, but take notes and check a couple wallpaper sources before making your choice. Get “extra rolls” with fancy patterns and make sure the production lots are the same for each roll purchased. You don’t want color mismatch because you mixed source lots.
With the hard part done, follow hanging directions coming with paper chosen.