The sensible, thrifty way to polish your silver (environmentally sound also, of course) is to eschew fancy chemical polishes that are near ten dollars (or crazy electrosometingorrather sink systems like the one my mom got scammed into when I was a kid) and simply take your nearly-finished toothpaste tube- the one that you've rolled already and have extracted every last possible morsel- and slice it up the side to the mouth and lay it flat as possible, and use a rag (you've hopefully been collecting holey shirts and socks for this purpose) to collect the remaining toothpaste, and polish away. Severe tarnish will take some scrubbing, but you should start to see shine come through the very dullest silver fairly quickly.
Left, unpolished (dull, blah) teapot. Right, post-toothpaste-treatment (bright! shiny!) teapot (please pardon crappy cell phone photo)
This trick works with nearly all kinds of toothpaste (save, perhaps, berry childrens' with crazy sweeteners and that sort of thing) from plain white to gel-ly blue. It's quite remarkable, and a great use of something you'd usually just throw in the trash. Wash in warm water and dry with a kitchen towel and you'll have your coveted shinyliciousness back! Repeat anytime your pieces start to look dull again- save your toothpaste tubes for a silver-polishing day! Which, by the way, you should schedule any time you have a cold. Inhaling menthol as you rub tarnish away leaves your nasal passages... very... clear.
If you have any special awesome thrifty hints, please share them- I might publish yours on the Cambridge MA Thrifty Living Examiner page- More info TBD!
Happy Saturday Night!