You can restain wood furniture, but in most cases you will first need to remove the old layer of stain. Furniture is rarely stained with the expectation that more layers of stain will be added later on. Trying to put new stain on old stain results in a sticky residue and a cloudy grain. Restaining requires the removal of the first layer of paint, varnish or stain.
First you must remove the finish on top of the wood. This is one of the most time-consuming steps and typically requires the use of a chemical stripper. Chemical solvents are effective at removing finish layers, but be sure to properly ventilate the project area to avoid fume issues. The more complex and heavily stained the furniture is, the longer this step will take.
After you have removed the stain with paint strippers, you will need to sand the wood. For furniture, a light sanding by hand is typically sufficient. There are several reasons for this step. You must smooth out any rough surfaces you created while stripping away the finish. You also need to remove any stain that has sunk down into the wood and reveal the natural grain before you can move on to adding the new layer of stain.
Once the wood is fully sanded you can choose nearly any type of stain you want for the restaining. There are oil-based stains that sink into the grain permanently, darkening the wood and bringing out the pattern. There are also lighter water-based stains, thick gel stains and combinations of stains and finishes that change color while creating a protecting layer. If your furniture is made from different types of wood, look for a stain that will make it easy to blend the wood types together. You can add extra layers in certain areas to darken the stain if necessary. A rag or brush is usually enough to apply most stains, but also follow the directions provided with the stain, including any ventilation requirements.
If you have a wood that cracks at the grain over time, you may also want to use a grain filler -- a common step for older oak or mahogany furniture. If you are working with a porous wood, you may want to consider using a sander sealer before you stain, which helps prime the wood for the new layer of finish.