The idea of removing wallpaper from paneling can be daunting. Don't fear. Removing wallpaper from paneling is actually easier than removing it from drywall. This is because you don't have to worry about gouging the underlying sheet rock. The method of removing wall covering from paneling will lead you through this process painlessly.
Start by clearing the area of furniture and anything else that will get in the way. Lay plastic sheeting along the base of the paneled wall. Tape it to the baseboard if you can. Remove switch plate covers and use plastic and masking tape to seal up the openings.
Try stripping the paper off the wall before wetting it down. Sometimes if you can find a loose corner to start with, the outer layer of wallpaper will peel off in large sheets. That's very satisfying! If it comes off easily, you will probably be left with the backing paper and glue but that is usually fairly easy to remove.
Mix up some wallpaper removal solvent. Sometimes just plain water works fine, if you're lucky. Otherwise use any of the following: commercial wallpaper remover, mix as directed on the bottle. Fabric softener can work too, add one cup to a gallon of warm water. Or try white vinegar mixed 50/50 with water. Ammonia can also work although the fumes might really get to you.
Working in sections about four feet square, soak the wallpaper, or the backing if you were able to peel the paper off. It is important to get it quite saturated, and give it about ten minutes to loosen the underlying glue. Use the putty knife to scrape the paper off the wall, letting it fall onto the plastic. You may have to go over sections two or even three times with a wet sponge to get it all off.
Wash the glue off the walls. If it is particularly stubborn, use a BBQ grill scrubber dipped in solvent. This usually works very well, but test a small area first to make sure you are not scratching the underlying wood finish. Pay attention to the grooves in the paneling, where glue residue can accumulate. Rinse the walls with the large sponge and clean water.
Go over the paneling one more time to really get all remaining glue residue off. If you are down to unpainted wood paneling, you can now do a final clean with wood-friendly soap like Murphy's oil to bring back the shine. Roll up the plastic sheeting. Hopefully all the old paper and glue residue landed along the plastic to you can ball it up and throw it way without leaving any extra mess to clean up.
Skip the Murphy's oil soap step if you are planning to paint the paneling. Search this site for instructions on how to paint paneling.