Allow your fireplace to cool to room temperature and shovel out the ashes and coals. Vacuum out any remaining dust so that when you apply the mortar, it will adhere to the firebox.
Mix water into the refractory mortar per the manufacturer's specifications. One tub of clay will be more than enough to patch up a residential firebox.
Spread the refractory mortar around the cracks. Use your fingers to force it into the cracks, then use a putty knife to smooth over the putty. Use as much putty as necessary to patch up the cracks; it is better to use more to make sure the cracks are completely filled than to leave any doubt.
Allow at least two days for the putty to dry and adhere to the firebox before lighting a fire in your fireplace.