Hi Roseblush, and thank you for posting your question on our forum.
Here's some cleaning tips to try to remove the stains from your white furniture. They start from fairly mild to increasingly stronger cleaning solutions.
We recommend you always test first on an inconspicuous spot and wear gloves to protect your hands. Wet a cloth in the solution, wipe, rinse and dry.
1) Try wiping the furniture with a solution of dishwashing detergent (we like Dawn, due to its grease cutting ability) and water. Try a teaspoon of Dawn to a gallon of water. Wipe the surface of the furniture with a cloth dipped in the cleaning solution, rinse and wipe dry.
2) If the stain persists, mix a few drops of ammonia with 3% hydrogen peroxide. Apply to the furniture in an inconspicuous spot first (to test), and rinse and wipe dry.
3) 1/2 cup of 20 Mule Team Borax
2 gallons of hot water
1/2 tsp of liquid dish detergent
1 tbs ammonia
4) You can also try TSP (trisodium phosphate).
This is a very powerful agent that is used by companies that repair smoke/water damage to walls and furnishings. It easily and completely removes nicotine/smoke stains. The product is available in a powdered form in many grocery and home improvement stores. A very small amount (1 tsp) is mixed with 1 gallon of water. The product is wiped on and then rinsed off with clean water. It is very strong and effective but be cautious and test it in an inconspicuous place first and follow the manufacturers instructions as it can cause paint/metal damage.
Good luck, and let us know how your project turns out!