Sand through the finish. Most antique or older pieces will have several layers of varnish, even if the wood has a patina. This will need to be removed. Use medium to harsh grade sandpaper, and start in a small area. Work until all trace of the varnish is removed, and then move to the next spot. If the varnish will not come off, you may need to use a chemical stripper or a heat gun.
Sand in the crevices. If the furniture piece has carving or detail work, you will also need to get into these small crevices. Sandpaper is typically difficult to use in this small of a space. Instead, use steel wool or a small sanding attachment on a rotary tool.
Sand down past the original stain of the wood. This may require an electric sander, especially if several coats of stain were used. Go slowly, and do not apply the sander heavily. Work in small strips until the entire piece matches in color and feels level to the touch.
Re-stain the piece. Use your desired color of stain for the wood. Use a small paint brush, and apply a very thin coat of stain to the wood. Allow this six to eight hours to dry. Sand the piece lightly with a fine grade of sandpaper. Repeat until the furniture piece has reached the desired color. Use a small paint brush to get into the crevices if any are present.
Protect the wood. In order to keep the piece from displaying a patina in the future, and to prevent damage, apply one to two coats of clear polyurethane. Work slowly and avoid getting air on the piece as it dries, as this will create bubbles in the clear coat surface. Sand in between coats.