Cleaning the blackened surface of silver that has been in a fire requires patience, persistence, and a gentle touch. Tempting though it may be to force your way through layers of oxidized tarnish, the best way to restore the sheen of your silver is to use the methods you rely on ordinarily. What has happened to blacken your silver is a dramatic and rapid episode of the darkening which occurs whenever silver is exposed to the sulfur compounds present in ordinary air and massively increased by combustion.
Wash blackened silver, as you would after ordinary use, using warm water, a soft sponge and liquid dish detergent. This will not remove tarnish but will remove surface grease, fire-preventive chemical residue or carbon residue from smoke. Silver may also have been damaged by water immersion, including whatever substances the water contained. The water will likely turn black as you clean the outer surface of your silver; prepare to repeat the process until the water remains clear.
Apply silver polish as usual with a soft sponge, let it dry and wipe it off with paper towels or rags. If you ordinarily work polish into intricate areas with an old soft toothbrush or cotton Q-tips, do so, but do not apply more than ordinary pressure or friction. Be prepared to repeat this process a number of times to remove the heavy accumulation of tarnish. Wash silver between polishing coats.
Use the aluminum-soda-salt-water method as an alternative or supplementary way to remove tarnish gently. Fill an old aluminum pot (or a stainless steel pot loosely lined with a sheet of aluminum foil) with boiling water and submerge our silver in the water. Add 1/4 to 1/2 cup baking soda (some people add 1 to 2 tbsp. salt, although the Society of American Silversmiths warns that salt can be very corrosive to silver). Let the soda froth completely. Drain the water and remove your silver. You should notice some lessening of tarnish. Again, be prepared to repeat the process several times to remove very heavy tarnish. This old kitchen-chemistry solution works well on ornate pieces because it lessens the rubbing needed to remove tarnish. Do not put old silver table knives into the solution because heat may damage the joints between the handle and the blade.
Examine silver for fire and tarnish-removal damage that you cannot solve at home. A strong grayish or pinkish tinge to silver-plated objects suggests that the plating has been worn thin enough to expose the base metal underneath. Fire damage may also include pitting or extremely stubborn streaks that require professional help.