Remove the legs or pegs. If at all possible, remove the legs or pegs from the furniture before you begin refinishing the legs or pegs. This makes it much easier to work. If you cannot do this, take the furniture out to an outside work area, and place it up on a raised surface -- this will help you reach everything much more easily.
Sand down the wood. Use a medium-grade sandpaper to get through the original finish of the wood. If you will not be staining the wood, use a fine grade of sandpaper instead.
Fill in cracks and holes with wood putty. Get wood putty that matches the finish on the wood as closely as possible. Use this to fill in any cracks or holes. Scrape away any excess putty with a plastic putty knife.
Sand the surface gently. You can hide your patch by sanding it down level with the rest of the leg. Use a fine grain of sandpaper for this job.
Polycoat the leg. Use a clear polyurethane to protect the work you've just done and the rest of the leg. Apply a clear polycoat with a paint brush, and let it dry. If you will be using more than one coat, sand it lightly before applying the second coat.
Re-attach the leg or peg. This is a good time to make sure that the leg or peg is not wobbly. Put the piece back together. If it appears wobbly, use a little more wood putty to fill in the joint and make the leg or peg more secure. Scrape away the excess with a putty knife.