There are a few things you can do to prevent hair dye from sticking to your wooden surfaces. Firstly, opt for dying your hair in the washroom instead of doing it somewhere else in the house. Still, if you must do it in a room where your wooden floors and surfaces are, it is a good idea to put down some old towels/rags, newspaper, or plastic sheets to catch any drips or spills. Secondly, avoid contact between your hair and any wooden surfaces as much as possible by wearing a shower cap or other type of head covering while waiting for the dye to set in your hair. Finally, clean up any spots or drips as soon as possible.