Safe & Simple paste remover
When I remove wallpaper, I try to remove the top of the paper first, usually pulling it off dry if I can, without using a paper tiger to prevent holes being punched into the wall to be repaired later. If I have to score the paper to get water underneath to remove the top layer, I will use a 40-60 grit sanding sponge. This helps to avoid putting lots of pin holes into the wall. Then I use a quart pump up garden sprayer (for small jobs) or a 1-2 gallon pump up sprayer (for larger jobs) and continually wet the paper down until I can start carefully pull it off. My objective is to do as little damage to the wall underneath to avoid lots of repairs later.
Sometimes the top layer of wallpaper will pull off dry and in sheets. After doing this, I spray the paper backing down until it will easily pull of in sheets. I will use a 6" spackle knife if necessary.
When I get all the paper off, the only thing left will be the wallpaper paste. I used to just spray this down repeatedly with hot water, then use a green Scotch Brite pad to loosen the paste, then wipe the past off with a grout cleaning sponge (you can find these yellow-orange sponges in the flooring materials area of Home Depot, Lowe's or a tile store. They are very absorbant and rinse well very quickly.) You will know that the paste is all gone when the walls stops feeling slimy and instead feels squeeky clean.
I used to just use hot water to wet the paste down, but the last couple of paper removal jobs I did I used Safe & Simple #603 paste remover and I have to say that it does make a difference in speed:
After all the paste is off and the walls are dry you can determine how damaged they are. I usually like to seal off the damaged areas with Gardz sealer before doing any repairs with mud so that the drywall does not start to melt from the water. Good luck,