I'm terrible when it comes to storing my jewelry. It's usually sitting in a little pile on my dresser, and of course looks tarnished and dull. Luckily I've got a quick way to fix it.
Sterling silver is so pretty when it's all polished and shiny but it does unfortunately tarnish. One of the best ways to keep it looking nice is to store it in a sealed container or a baggie. When I actually remember to do this I'm always impressed at how long it lasts.
I've also read that you can store it with a piece of chalk or activated charcoal. There's also anti tarnish strips that will do the job.
If you're like me and leave it laying out, then a polishing cloth is a great way to bring back the shine and remove any light tarnishiing. I actually include a small polishing pad with each order I send out. Those little suckers are awesome!
You can also just wash the piece in a little dish soap and water. Be sure to use a gentle soap like Dawn.
If you've got a piece that's really tarnished try this easy method using baking soda:
Line a small baking pan or glass dish with aluminum foil. Add about one cup of boing water and about a tablespoon of baking soda. Then place the piece in the solution. It should work fairly quickly but you can let it soak for a few minutes then rinse with water.
I've done this with just heating the water in the microwave and sometimes I add a little white vinegar too. If you use vinegar be aware it will get pretty fizzy, so be careful when adding it to boiling water.
Most of the time just wiping your jewelry with a soft cloth or just rubbing with your fingers will shine it up nicely, too.
The one thing I would not recommend is using bleach. I've seen this mentioned before but it's way to harsh and can harm your jewelry.