Depending on the piece of furniture if it is painted, I will often try using a hot air heating gun to remove several layers of paint at one time. I find this method takes off a lot of paint without the mess of a chemical liquid or paste stripper. A lot depends on the type of paint used. The type of wood used is also important. Some paints will sink deep into many types of wood especially softwoods such as pine.
Special care needs to be given when removing paint from old veneer.
After removing the old paint, much of the wood should now be exposed. At this point, I follow up with several coats of a chemical semi-paste stripper. The longer the stripper stays on the wood, absorbs into the wood, generally the easier it will be to remove the paint with a course steel wool. You may have to repeat this procedure several times to remove all the paint. I do not buy the most expensive cleaner.