Your jewellery will tarnish much less if you keep it in a small plastic zip lock bag or some kind of air tight container and keep it away from the air and humidity.
If it does tarnish, you can clean it in this non toxic manner, good for silver items without stones or pearls:
Put tinfoil shiny side up is a glass bowl. Cover the bottom with baking soda, add the jewellery and pour boiling water over the lot. Watch the magic happen. Make sure to rinse well and DRY the silver after.For items with stones or pearls, I am partial to Haggerty's silver foam.
Also keeping a jewellers cloth on hand can be a simple way to keep your jewellery polished.
Pearls should be kept away from perfumes and house hold cleaning agents.
Beaded items will have to be restrung once in a while.
For further information you could take a look at my blog about polishing.