Widen the crack with a chisel. This cleans out the cracked area and will help the wood putty form a better bond.
Fill in the crack with wood putty. Use a putty knife and scrape on a thin layer of wood putty into the crack. Scrape off the excess with the edge of the putty knife. Let this set until it is hard to the touch. Apply another coat of putty to the wood if necessary.
Sand the patched area with a fine-grit sanding block. Smooth out any ridges in the putty. Check that the patched area is level with the rest of the wood.
Apply a thin coat of wood stain over the patched area with a paintbrush to match the color of the existing railing. Brush on a thin coat with the grain of the wood. Let it dry for at least four to six hours.
Apply a coat of polyurethane over the patch. Brush on a thin coat of non-yellowing polyurethane. Let it dry for six to eight hours before allowing foot traffic on the stairs.