I have silver jewellery and I use a very cheap method to make them sparkle.
You need 2 teaspoons of baking soda, boiling water, tin foil and a bowl. Lay the tinfoil on the bottom of the bowl, add the baking soda and enough water to make a paste. Then cover the jewellery with the paste and leave for 30 minutes. Depending on how dirty the piece is, it might need extra time. Also you might need to use an old toothbrush to help you along with the cleaning.