I inherited furniture from my parents. How do I remove the nicotine stains from the fine wood furniture without damaging the finish?
It's actually water-soluble. A wash with a household cleaner (spic-n-span) and a double rinse, then wipe dry and apply furniture wax.
Upholstery, OTOH, a different problem, probably fatal.
Additionally to Sombreuil's good advice: if there is bare wood anywhere on this piece, it will probably continue to stink of nicotine smoke. Areas inside the drawer cabinet or bottom of drawers are seldom finished and the nicotine penetrates deep into the wood. Here I would not even bother to try to wash the bare wood, but rather completely seal these surfaces with clear shellac. There is no better sealer of smell than shellac! This also works well for moldy smelling furniture which was stored for too long in a damp location.
I you are going to use Spic n Span, mix it with water first, to make it less abrasive.