You line a pan with aluminum foil, add hot water and then 2 c. baking soda and 1/4 c. salt and swirl it around and add the silver. It makes a chemical reaction that removes the tarnish. I had to look up the measurements since I haven't done it in a few years, but as I recall it worked pretty well.

Boil the heck out of the items, rinse well and polish w/metal cleaner. I've never tried it on silver before this. Worked like a charm. I have an old aluminum pan dedicated to just this process. The combination of salt and baking soda stains the pan so I'd advise anyone doing this to pick up an big old aluminum pot at a thrift shop. Save it for just this type of job.

I always make sure the item is totally covered with the solution.
Thanks Vinca for suggesting I use this for the silver. A rinse, then a good buff w/Wenol, the spoons look like new.