Clean your sterling silver jewelry just like you would your sterling silverware - with a good quality silver cleaner. I like Twinkle the best, and also the Wright's products, Silver Polish and Silver Cream. I much prefer the silver cream, as it comes in a little pot with a sponge and is not as runny as the polish. Just make a mixture of a little silver cleaner and water, and polish away. Then wash the piece of jewelry in a hot water rinse, then in a warm water mix with some gentle soap cleaner. Rinse again with hot hot water, and dry immediately. Of course, if your silver piece has any motors or batteries like a watch in it, you'll have to be very careful to only get the silver part wet.
All of those other quick and easy methods like plastic and the one where you dip silver in some solution are extremely dangerous to your silver, in my opinion. At least for silver flatware, anything that takes off the subtle discolorations known as "patina" are denigrating the quality of the piece. You want it clean and shiny but not glaring, if you know what I mean.
The cleaning cloths someone recommended are impregnated with cleaner and also work pretty well. I just don't trust anything on my silver except good old products I have used for years, and a little elbow grease!
There is no household job that is messier, but more rewarding, than polishing silver. It is just amazing how much difference you can make in 5 minutes with a clean cloth and a good rubbing!!!