The best way is to use a good silver polish. I inherited a lot of silver plate. My local jeweller said that a good silver polish is usually pink because it contains jewellers' rouge. He recommends Goddards silver cleaner. This is available in a lot of supermarkets and ironmongers. It is a dark blue tub of cleaner with a small sponge inside. Damp the sponge in warm water then dip it into the polish. Rub the silver, then rinse and dry. This is the safest way to clean plate. More abrasive polishes will wear the silver plate away.
Kim and Aggie also say that if you have no silver polish then toothpaste (a non-gel sort) will do the job. Apply on a soft cloth, rub well, rinse.
And there is a quick way, which uses electrolytic techniques. But it is best on solid silver. Take a plastic bowl e.g. a washing up bowl. Line it with aluminium foil. Add a couple of tablespoons of washing soda. Put the silver in the bowl. Cover with very hot water. Leave for 20 minutes or so. The water will froth a bit, and the tarnish mysteriously transfers from the silver to the foil. After the frothing stops, fish out the silver, rinse and dry. This method is only recommended for solid silver. But I have done it on my plate with no bad effects. But on your own head be it, if you care to try. To my mind the shine is not as deep as with the Goddard's polish but there is very little effort. I tend to use it with brown, tarnished silver. In subsequent cleanings I use Goddard's. Incidentally, if you have pieces which are deeply embossed or chased, the polish will leave some darker silver in the recesses. This highlights the embossing rather nicely. the electrolytic method will leave the piece uniformly clean and shiny. You may not want this effect.
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