Clean the entire piece of furniture, including the leather insert, with mild soap and water. Wipe down the furniture with a rag dampened with clean water.
Tape off the leather insert with low-tack painter's tape. Cover the insert with newspaper to protect it while you sand and stain the wood. Remove the hardware from the furniture. Tape off any other areas you do not wish to refinish.
Sand off the finish on the wooden parts of the furniture, using a palm sander or sanding by hand. A palm sander is a good choice because it works quickly and its circular motion sands evenly. Remove the finish until you are down to the bare wood. Remove the sanding dust with a damp rag.
Apply stain to the wood parts of the furniture, using a clean rag or a brush. Wipe away the excess stain with another rag. Continue applying and removing stain until you get the depth of color you want. Allow the stain to dry completely.
Remove the painter's tape and newspaper from the leather insert. Tape off the wood surrounding the leather insert to protect while you sand and dye the leather.
Put on a pair of gloves. Strip most of the original color from the leather insert with a leather prep product. Most leather prep is alcohol-based.
Sand the leather gently by hand, using fine-grit sandpaper. Use light pressure so you don't damage the leather. Wipe away any sanding residue with a damp cloth.
Apply the leather color with a sponge, using smooth, even strokes. Allow the first coat to dry. Apply a second coat. Add a third coat with the spray bottle included in many leather kits. The spray helps create even coverage. Allow the leather insert to dry for 48 hours.