how do you polish silverware at home?

Silver polish cream and a soft cloth, rubbing in straight lines rather than circles. Rinse in warm water and dry straight away, water spots show on silver. For a big drawer of it the foil bath is faster: line a bowl with foil, shiny side up, add a couple of spoons of baking soda, pour in very hot water and lay the pieces in touching the foil. The tarnish moves off in minutes. It also takes the dark out of engraved patterns though, which some people like keeping, and keep knives with glued hollow handles out of hot water. Store it in a cloth bag or with anti tarnish strips and you'll do this a lot less often.