Clean out the dent in the wood furniture with a small piece of sandpaper and vacuum. Rub the sandpaper in the wood dent and then vacuum out the dent so there is no loose debris.
Fill in the chipped area with a fill stick. Fill sticks are composed of a tinted waxy substance and can be purchased at most hardware stores. Match the color of the fill stick with the color of your furniture. The fill sticks come in large variety of colors, but if you cannot match the furniture color exactly, get a fill stick that is just slightly lighter or darker than the furniture color. Rub the fill stick into the area until it is about level with the surrounding wood.
Rub a clean dry cloth over the area until the fill stick matches the wood. Work carefully so you do not remove the fill stick.
Apply polyurethane over the area with a paintbrush. Let the polyurethane dry completely.
Gently rub the finished area with steel wool. The steel wool will help you to match the sheen of the polyurethane with the sheen of the surrounding area.