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Choose a water or oil based stain, depending on your desired finish. Get a clean paint brush, sponge, or foam brush. Open and stir the stain thoroughly. Test your stain in an inconspicuous area to ensure it looks good. Wipe the furniture with a damp cloth, then sand with 220 grit paper if using a water-based stain. Apply the stain in a thin, even coat. Make a final pass over the stain in the direction of the wood grain. Wipe the stain off with a clean cloth after it has soaked for your desired time. Let the wood dry for 6-8 hours.
While there are some hybrid stains, most people buy either water-based or oil-based stains. Water-based stains are non-toxic and easy to clean, but can cause some streaking if you're not careful. Oil-based stains are easier to apply evenly but produce stronger fumes and can be tough to clean. If the piece of furniture can easily be moved outside, to the garage, or to another easy-to-clean area, go with oil-based stains. You want something absorbent but soft. Foam brushes, especially those with a pointed edge to get in the corners, are your best bet. Clean, soft rags and towels will work as well, though they will be permanently colored by the stain. Make sure that is well mixed, following the instructions on the can. Be sure to keep the top as well, as you can close up the stain and save it for another project if there is any left. Find a hard-to-see area and apply a little stain in an square. Make sure it doesn't drip, then wipe it off after 4-5 minutes and check the color. Keep an exact measurement of the time you let it sit for. How does this stain work with the wood's natural color?  If you want the finished piece to be darker than this test area, you'll need to leave the stain on longer before wiping it off. If you want the finished piece to be lighter you'll have to wipe the stain off faster than you did for the test area. As wood absorbs moisture, it slightly expands. By getting the surface damp and then sanding down the small burrs or bumps that rise up, you better prepare the wood for your water-based stain. While optional, this step can even help with oil-based stains. It will result in a smoother finished surface. Use your rag, sponge, or brush to apply a thin, even layer of stain over the entire piece. Work slowly, only keeping a little stain on the brush at any one time to prevent dripping or pooling. It should be thin enough that the stain isn't running, just sitting on the furniture. You can apply the stain any way you want, but your last pass of the brush or rag should be along the direction of the grains. This ensures a beautiful, non-streaky final finish. Remember -- the longer you leave it on, the darker the color will be. While you can choose your timing based on your own desires, make sure that it doesn't dry on the wood. If it is starting to dry, wipe it off immediately -- you can also apply a second coat later on if  you desire a darker color. Check the stain's instructions to see if you need to wait even longer, though most stains will be dry within half a day or less. Try to place the wood in a well-ventilated area to speed up the process and prevent fumes from collecting.