For heavier tarnish, the gentlest effective route
For solidly blackened cutlery, the kitchen method many households swear by is a bath: line a heatproof bowl with aluminium foil, shiny side up, lay the silver so it touches the foil, sprinkle over bicarbonate of soda, and pour in very hot water to cover. The tarnish lifts through a simple chemical exchange rather than abrasion, which is why it works on the inside of forks and the crevices of decorative handles where no cloth reaches. Rinse well and dry completely.
Important caveats, though, and they matter. Do not use this on anything with a deliberately oxidised pattern, because the dark recesses are part of the design and once they're gone the detail flattens out. Keep it away from pieces with knife blades glued into handles, with pearls, shell, amber, coral, turquoise or any stone set in adhesive, and from anything antique and valuable enough that you'd regret guessing. For those, a specialist is the sensible call.
What to avoid entirely
Toothpaste, scouring powder and abrasive sponges all work in the sense that the black comes off, and all of them leave fine scratches that dull the surface permanently. Dishwashers are hard on silver and silver plate, and are particularly unkind to hollow-handled knives, where the heat can loosen the filling inside. Rubber bands, rubber gloves left in contact, wool and newspaper all accelerate tarnishing, so none of them belong in a storage box.
