Assess the damage to the stair stringers. Do you notice large cracks along the sides of the stairs? Do the cracks worsen when you put weight on the stairs? This means that your stringers need to be repaired.
Cut a piece of 2-inch-by-4-inch lumber in the same size as the cracked stair stringer using an electric saw or hand saw.
Apply wood adhesive to the face of the replacement lumber.
Apply the adhesive-coated side of the lumber to the damaged stair stringer. Use a clamp to secure the wood splint in place.
After the wood adhesive is dry, install screws around the four corners of the wood. This will serve to further reinforce the repair.
Test the repair carefully by adding weight to the stairs. There should be no visible cracks in the wood.