If wallpaper was removed from your walls in a poor manner, you may need to repair the damaged drywall. This can be accomplished with just a couple of tools that you most likely already have. In order for your new paint job to look good, these repairs must be made. If you are wallpapering the walls again, it won't be necessary.
Step 1--Preparing the Wall
If you have cuts or scratches in your drywall that aren't very deep or are just through the outside paper-like coating, you may be able to rub them out with the steel wool or fine sandpaper. Use light pressure and move the steel wool or sandpaper quickly along the length of the scratch or scrape to remove rough edges. This may be all it takes to ready the job for painting, as paint will fill in light scratches.
Step 2--Deep Cuts or Holes
If you have deep cuts or holes that the above technique won't fix, you will need to use the spackling compound. Pick up a bit of the compound on your putty knife and sweep it over the cut or into the hole, pressing lightly and keeping the putty knife moving as you fill in the area. You may need to go over it again in the opposite direction. Allow it to dry completely. Then rub smooth with a damp sponge to prepare for painting.