Line a shallow pan with alulimun foil. Place the silverplate on the foil and cover with a warm, salt water mixture. Let it stand over night in this mixture. There will be a odor from the oxidation, so you might want to put in the garage. Then start cleaning with a silver paste. You will be amazed at how easily the tarnish is removed. Have a few stubborn pieces, resoak them. Once again, i do not recommend for Grandma's prized pieces, unless there is no other alternative. In a pinch and do not have polishing paste, I have used toothpaste to shine some silverplate in a hurry.
A special cleaning solution can be made to clean without damage. Mix equal parts of acetone, and alcohol. Using a soft cloth or brush clean all parts of your silver. Make sure that you dry it with a soft cloth. This will leave your silver with some protection too.