Clean off gum, goo, grease or candle wax first. Start with gum or candle wax. Spray the affected area with carbon dioxide freezing spray as is used to clean computer keyboards. Once the wax or gum is frozen scrape it away very gently with a rubber spatula. Use benzine as an alternative to freezing spray. Follow the application directions on the can.
Clean grease, goo and other heavily soiled areas on the Danish furniture with a trisodium phosphate solution. Purchase this at a home improvement store. Follow the product instructions on the box for proportions. Mix the solution and dip the plastic brush in it. Scrub the soiled furniture focusing on the soiled spot. Do not spread the watery solution around the furniture, keep it centered at the greasy spot. Repeat the process until the soil is removed.
Oil very dry areas of the furniture with a coat of teak oil, mineral oil or lemon oil. Concentrate on the dry section only. Apply oil to a soft, clean cloth and work it into the area. Let is set for 10 minutes. Rub off any excess with a clean cloth. Repeat this until the dry section is no drier than the rest of the piece.
Clean the entire piece of furniture once the most heavily soiled and driest sections have been treated. Wipe down the table with a soft, water-dampened cloth. Make sure it is not wet, just damp. Use a lot of elbow grease to rub off the surface dirt.
Oil the entire piece of furniture with teak, mineral or lemon oil. Apply generously to a clean cloth and dab on to every area, making sure you do not miss corners and crevices or areas near hardware. Wait 10 minutes. Rub off the excess oil with another clean cloth. Re-oil if needed or buff to a high shine.