It can be extremely frustrating after purchasing that brand new pair of leather shoes and wearing them a couple of times to find a deep scuff mark on them. Fortunately, there are a number of products -- both commercial items designed specifically for your shoes, and household products found in your kitchen pantry and bathroom cabinet -- that can remove that scuff mark and make those leather shoes look brand new again.
Verify what you have is indeed a scuff and not a cut or gouge in the shoe. Take the shoe to a cobbler for repair if what you have is not a scuff mark.
Erase the scuff using a pencil or artist eraser as your first attempt. Use caution and only apply light pressure on the surface of the scuff so as to not rub a bare spot into the leather.
Add a dab of petroleum jelly to a clean rag and apply to the surface of the scuff. Rub the jelly into the shoe vigorously and allow to rest on the surface of the shoe for a couple of hours. Wipe away any excess and buff the shoe.
Place a small amount of paste toothpaste on an old toothbrush or small brush. Brush the scuff in a circular motion, then rinse the shoe with water. Dry the surface of the shoe immediately and buff the shoe's surface.
Use the recommended shoe polish for your shoe and apply with a polishing pad or brush in a circular motion. Allow the polish to dry fully, then buff the polish away. Use cream leather conditioner if polish is not available or did not remove the scuff fully.
Spray refinishing spray on the surface of the scuff if you have dark scuffs showing up on light or white shoes. Allow the spray to soak in, then remove any excess with a clean cloth. Polish and buff your shoes immediately afterward.