You can use tarnish-resistant flannel cloth to polish your silverware in a pinch. Simply rub the silverware vigorously with a piece of dry cloth -- wetting the chemically treated cloth will ruin it -- and your silver will definitely look brighter. You'll get even better results, however, if you use regular silver polish.
To polish vintage flatware with Bakelite plastic handles, use a sponge or soft cloth to rub on some Novis plastic polish, available at hardware and homeware stores. You can polish the stainless-steel blades of flatware with Bakelite, bone, ivory, or mother-of-pearl handles by sprinkling a bit of regular household cleanser on the blades and rubbing vigorously with a cloth. (Avoid getting cleanser on the handles, however, as its abrasiveness will dull and scratch them.) Never wash these items in a dishwasher, as you may loosen the connection between handle and blade.