My favorite set of flatware was my grandmother's and it's stainless steel, but has dulled over the years. I just searched and found this tip from Heloise:
The old-fashioned hint is to soak the flatware in hot water mixed with a splash of ammonia (one teaspoon per gallon). Rinse with clear, hot water and dry well with a clean, soft cloth. But today specially formulated stainless steel cleaners or polishes can do the job too. To prevent your flatware from discoloring in the future, rinse the pieces immediately after use. Foods like lemon, salt, mayonnaise or mustard can cause corrosion or pitting. Your stainless steel can be put in the dishwasher (although not with sterling silver in the same compartment), but hand-washing is better for preserving the shine. Follow these hints: Don't soak for long periods; never pour detergent directly on the pieces; wash in hot water; dry immediately.