Sand the nicked area with fine-grit sandpaper if there are any rough edges.
Pour some mineral spirits on a rag and clean the nicked area thoroughly.
Put some wood putty onto the putty knife and fill in the entire area of the nick. Make sure there is enough putty to fill in the nick completely. Let it dry completely, which should take at least an hour. If the wood putty shrinks below the surface, apply some more and let it completely dry.
Smooth down the surface with sandpaper until it is flat.
Apply a stain with a rag to match the color or tone of the rest of the wood.